ASTM E722-19

Standard Practice for Characterizing Neutron Fluence Spectra in Terms of an Equivalent Monoenergetic Neutron Fluence for Radiation-Hardness Testing of Electronics

SIGNIFICANCE AND USE
5.1 This practice is important in characterizing the radiation hardness of electronic devices irradiated by neutrons. This characterization makes it feasible to predict some changes in operational properties of irradiated semiconductor devices or electronic systems. To facilitate uniformity of the interpretation and evaluation of results of irradiations by sources of different fluence spectra, it is convenient to reduce the incident neutron fluence from a source to a single parameter—an equivalent monoenergetic neutron fluence—applicable to a particular semiconductor material.  
5.2 In order to determine an equivalent monoenergetic neutron fluence, it is necessary to evaluate the displacement damage of the particular semiconductor material. Ideally, this quantity is correlated to the degradation of a specific functional performance parameter (such as current gain) of the semiconductor device or system being tested. However, this correlation has not been established unequivocally for all device types and performance parameters since, in many instances, other effects also can be important. Ionization effects produced by the incident neutron fluence or by gamma rays in a mixed neutron fluence, short-term and long-term annealing, and other factors can contribute to observed performance degradation (damage). Thus, caution should be exercised in making a correlation between calculated displacement damage and performance degradation of a given electronic device. The types of devices for which this correlation is applicable, and numerical evaluation of displacement damage are discussed in the annexes.  
5.3 The concept of 1-MeV equivalent fluence is widely used in the radiation-hardness testing community. It has merits and disadvantages that have been debated widely  (9-12). For these reasons, specifics of a standard application of the 1-MeV equivalent fluence are presented in the annexes.
SCOPE
1.1 This practice covers procedures for characterizing neutron fluence from a source in terms of an equivalent monoenergetic neutron fluence. It is applicable to neutron effects testing, to the development of test specifications, and to the characterization of neutron test environments. The sources may have a broad neutron-energy range, or may be mono-energetic neutron sources with energies up to 20 MeV. This practice is not applicable in cases where the predominant source of displacement damage is from neutrons of energy less than 10 keV. The relevant equivalence is in terms of a specified effect on certain physical properties of materials upon which the source spectrum is incident. In order to achieve this, knowledge of the effects of neutrons as a function of energy on the specific property of the material of interest is required. Sharp variations in the effects with neutron energy may limit the usefulness of this practice in the case of mono-energetic sources.  
1.2 This practice is presented in a manner to be of general application to a variety of materials and sources. Correlation between displacements (1-3)2 caused by different particles (electrons, neutrons, protons, and heavy ions) is out of the scope of this practice but is addressed in Practice E3084. In radiation-hardness testing of electronic semiconductor devices, specific materials of interest include silicon and gallium arsenide, and the neutron sources generally are test and research reactors and californium-252 irradiators.  
1.3 The technique involved relies on the following factors: (1) a detailed determination of the fluence spectrum of the neutron source, and (2) a knowledge of the degradation (damage) effects of neutrons as a function of energy on specific material properties.  
1.4 The detailed determination of the neutron fluence spectrum referred to in 1.3 need not be performed afresh for each test exposure, provided the exposure conditions are repeatable. When the spectrum determination is not repeated, a neutron fluence monit...

General Information

• Status: Published
• Publication Date: 30-Sep-2019
• ICS: 31.080.01 - Semiconductor devices in general
• Technical Committee: E10 - Nuclear Technology and Applications
• Drafting Committee: E10.07 - Radiation Dosimetry for Radiation Effects on Materials and Devices

Relations

• Replaces: ASTM E722-14 - Standard Practice for Characterizing Neutron Fluence Spectra in Terms of an Equivalent Monoenergetic Neutron Fluence for Radiation-Hardness Testing of Electronics
• Effective Date: 01-Oct-2019
• Refers: ASTM E265-15(2020) - Standard Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32
• Effective Date: 01-Jul-2020
• Refers: ASTM E944-19 - Standard Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance
• Effective Date: 01-Oct-2019
• Refers: ASTM E844-18 - Standard Guide for Sensor Set Design and Irradiation for Reactor Surveillance
• Effective Date: 01-Jun-2018
• Refers: ASTM E170-17 - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 01-Jun-2017
• Refers: ASTM E170-16a - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 01-Oct-2016
• Refers: ASTM E170-16 - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 15-Feb-2016
• Refers: ASTM E170-15a - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 01-Sep-2015
• Refers: ASTM E265-15 - Standard Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32
• Effective Date: 01-Jun-2015
• Refers: ASTM E170-15 - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 15-Mar-2015
• Refers: ASTM E170-14a - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 15-Oct-2014
• Refers: ASTM E170-14 - Standard Terminology Relating to Radiation Measurements and Dosimetry
• Effective Date: 01-Sep-2014
• Refers: ASTM E844-09(2014)e2 - Standard Guide for Sensor Set Design and Irradiation for Reactor Surveillance
• Effective Date: 01-Jun-2014
• Refers: ASTM E844-09(2014)e1 - Standard Guide for Sensor Set Design and Irradiation for Reactor Surveillance, E 706 (IIC)
• Effective Date: 01-Jun-2014
• Refers: ASTM E944-13e1 - Standard Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance
• Effective Date: 01-Jan-2013

Overview

ASTM E722-19 is a standard practice developed by ASTM International for characterizing neutron fluence spectra using an equivalent monoenergetic neutron fluence, specifically for radiation-hardness testing of electronics. This standard provides methods to unify and simplify the interpretation of radiation hardness test results for semiconductor devices exposed to varying neutron sources. By representing the neutron fluence as a single equivalent parameter, it supports consistent comparison and specification of neutron-induced damage across different facilities and irradiation conditions.

Key Topics

• Neutron Fluence Spectrum Characterization: Offers a standardized approach to reduce complex neutron spectra to an equivalent monoenergetic neutron fluence (often at 1-MeV), making test results comparable.
• Displacement Damage Evaluation: Focuses on displacement damage in semiconductor materials (such as silicon and gallium arsenide) resulting from neutron irradiation, which is a key mechanism in device performance degradation.
• Material-Specific Application: Emphasizes the importance of the semiconductor material in use, since the correlation between displacement damage and observed electrical degradation can vary.
• Use of Neutron Monitors: Encourages the use of monitor foils (e.g., activation foils or sensors) for routine monitoring when irradiation conditions are repeatable, ensuring ongoing test consistency.
• Equivalence and Limitations: The practice is applicable for neutron sources with energies up to 20 MeV (not valid for displacement damage primarily from sub-10 keV neutrons), and acknowledges potential limitations in correlating calculated displacement damage with all device performance parameters.

Applications

ASTM E722-19 is widely used in:

• Radiation-Hardness Testing: Employed by semiconductor manufacturers, research labs, and military agencies for predicting the performance and durability of electronic components in neutron-rich environments.
• Neutron Test Environment Characterization: Provides a framework for evaluating and specifying the neutron exposure conditions in test facilities such as reactors and californium-252 irradiators.
• Development of Test Specifications: Assists engineers and scientists in drafting specifications and acceptance criteria for device radiation tolerance, based on a consistent definition of neutron fluence.
• Comparative Analysis: Enables unified reporting and benchmarking of test results from different sources or facilities by reducing variable spectra to the equivalent 1-MeV neutron fluence.
• Material-Specific Hardness Assurance: Supports control and validation of radiation hardness in devices made from specific materials like silicon and gallium arsenide.

Related Standards

Several other ASTM and international documents are referenced or complement the use of ASTM E722-19 in neutron effects testing:

• ASTM E170: Terminology Relating to Radiation Measurements and Dosimetry
• ASTM E265: Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32
• ASTM E693: Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels
• ASTM E720: Guide for Selection and Use of Neutron Sensors
• ASTM E721: Guide for Determining Neutron Energy Spectra
• ASTM E844: Guide for Sensor Set Design and Irradiation for Reactor Surveillance
• ASTM E944: Guide for Application of Neutron Spectrum Adjustment Methods
• ASTM E3084: Practice for Characterizing Particle Irradiations in Terms of Non-Ionizing Energy Loss (NIEL)
• ICRU Reports 13, 60, 85: Definitions and units for neutron fluence and radiation quantities

Practical Value

Through standardizing the method to determine equivalent monoenergetic neutron fluence, ASTM E722-19 ensures that radiation hardness testing of electronics is both uniform and technically reliable. This allows organizations to accurately predict and report device resilience in neutron environments, facilitating regulatory compliance, mission assurance, and robust electronics design for critical applications in aerospace, defense, nuclear energy, and high-energy physics.

Keywords: neutron fluence, monoenergetic neutron, radiation hardness, semiconductor damage, silicon, gallium arsenide, displacement damage, electronics testing, hardness parameter, 1-MeV equivalent fluence.

Standards Content (Sample)

This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the
Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
Designation: E722 − 19
Standard Practice for
Characterizing Neutron Fluence Spectra in Terms of an
Equivalent Monoenergetic Neutron Fluence for Radiation-
Hardness Testing of Electronics
This standard is issued under the fixed designation E722; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision.Anumber in parentheses indicates the year of last reapproval.A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope neutron source, and (2) a knowledge of the degradation
(damage)effectsofneutronsasafunctionofenergyonspecific
1.1 This practice covers procedures for characterizing neu-
material properties.
tron fluence from a source in terms of an equivalent monoen-
ergetic neutron fluence. It is applicable to neutron effects 1.4 The detailed determination of the neutron fluence spec-
testing, to the development of test specifications, and to the trum referred to in 1.3 need not be performed afresh for each
characterizationofneutrontestenvironments.Thesourcesmay testexposure,providedtheexposureconditionsarerepeatable.
have a broad neutron-energy range, or may be mono-energetic When the spectrum determination is not repeated, a neutron
neutron sources with energies up to 20 MeV. This practice is fluence monitor shall be used for each test exposure.
not applicable in cases where the predominant source of
1.5 The values stated in SI units are to be regarded as
displacement damage is from neutrons of energy less than 10
standard. No other units of measurement are included in this
keV. The relevant equivalence is in terms of a specified effect
standard, except for MeV, keV, eV, MeV·mbarn, rad(Si)·cm ,
on certain physical properties of materials upon which the 2
and rad(GaAs)·cm .
source spectrum is incident. In order to achieve this, knowl-
1.6 This standard does not purport to address all of the
edge of the effects of neutrons as a function of energy on the
safety concerns, if any, associated with its use. It is the
specific property of the material of interest is required. Sharp
responsibility of the user of this standard to establish appro-
variations in the effects with neutron energy may limit the
priate safety, health, and environmental practices and deter-
usefulness of this practice in the case of mono-energetic
mine the applicability of regulatory limitations prior to use.
sources.
1.7 This international standard was developed in accor-
1.2 This practice is presented in a manner to be of general
dance with internationally recognized principles on standard-
application to a variety of materials and sources. Correlation
ization established in the Decision on Principles for the
between displacements (1-3) caused by different particles
Development of International Standards, Guides and Recom-
(electrons, neutrons, protons, and heavy ions) is out of the
mendations issued by the World Trade Organization Technical
scope of this practice but is addressed in Practice E3084.In
Barriers to Trade (TBT) Committee.
radiation-hardnesstestingofelectronicsemiconductordevices,
specific materials of interest include silicon and gallium 2. Referenced Documents
arsenide, and the neutron sources generally are test and
2.1 ASTM Standards:
research reactors and californium-252 irradiators.
E170Terminology Relating to Radiation Measurements and
Dosimetry
1.3 The technique involved relies on the following factors:
(1) a detailed determination of the fluence spectrum of the E265Test Method for Measuring Reaction Rates and Fast-
Neutron Fluences by Radioactivation of Sulfur-32
E693Practice for Characterizing Neutron Exposures in Iron
1 and Low Alloy Steels in Terms of Displacements Per
This practice is under the jurisdiction of ASTM Committee E10 on Nuclear
Technology and Applicationsand is the direct responsibility of Subcommittee Atom (DPA)
E10.07 on Radiation Dosimetry for Radiation Effects on Materials and Devices.
Current edition approved Oct. 1, 2019. Published October 2019. Originally
approved in 1980. Last previous edition approved in 2014 as E722–14. DOI: For referenced ASTM standards, visit the ASTM website, www.astm.org, or
10.1520/E0722-19. contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM
The boldface numbers in parentheses refer to a list of references at the end of Standards volume information, refer to the standard’s Document Summary page on
this practice. the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E722 − 19
E720Guide for Selection and Use of Neutron Sensors for mean atomic mass of the material andΦ is the neutron fluence
Determining Neutron Spectra Employed in Radiation- from a monoenergetic source of energy E.
Hardness Testing of Electronics
3.1.2.1 Discussion—This quantity may be calculated from
E721Guide for Determining Neutron Energy Spectra from the microscopic neutron interaction cross sections, the kine-
Neutron Sensors for Radiation-Hardness Testing of Elec-
matic relations for each reaction and from a suitable partition
tronics function which divides the total kerma into ionization and
E844Guide for Sensor Set Design and Irradiation for
displacement kerma. The use of the term microscopic kerma
Reactor Surveillance factor in this standard is to indicate that energy times area per
E944Guide for Application of Neutron Spectrum Adjust-
atom is used, instead of per unit mass, as in the term kerma
ment Methods in Reactor Surveillance factor defined in E170.
E3084Practice for Characterizing Particle Irradiations of
3.1.3 fluence spectrum hardness parameter—(H
Eref,
Materials in Terms of Non-Ionizing Energy Loss (NIEL)
mat=Φ /Φ) this parameter is defined as the ratio of the
eq,Eref,mat
2.2 International Commission on Radiation Units and Mea- equivalent monoenergetic neutron fluence to the total fluence,
surements (ICRU) Reports: Φ /Φ.Thenumericalvalueofthehardnessparameteris
eq,Eref,mat
ICRU Report 13Neutron Fluence, Neutron Spectra, and also equal to the fluence of monoenergetic neutrons at the
Kerma specific energy, Eref, required to produce the same displace-
ICRU Report 60Fundamental Quantities and Units for ment damage in the specified material, mat, as unit fluence of
Ionizing Radiation neutrons of neutron spectrum Φ(E).
ICRU Report 85Fundamental Quantities and Units for 3.1.3.1 Discussion—For damage correlation, a convenient
Ionizing Radiation (Revised)
method of characterizing the shape of an incident neutron
fluence spectrum Φ(E), is in terms of a fluence spectrum
3. Terminology
hardness parameter (4).The hardness parameter in a particular
neutron field depends on the displacement damage function
3.1 Definitions of Terms Specific to This Standard:
used to compute the damage (see annexes) and is therefore
3.1.1 displacement damage function—(F (E)) an
D,mat
different for different semiconductor materials.
energy-dependentparameterproportionaltothequotientofthe
observable displacement damage per target atom and the 3.1.4 equivalent monoenergetic neutron fluence—(Φ
eq,Eref,
neutron fluence. Different displacement-related damage func- mat) an equivalent monoenergetic neutron fluence, Φ ,
eq,Eref,mat
tions may exist, so the damage mode of interest and the characterizes an incident fluence spectrum, Φ(E), in terms of
observation procedure shall be identified when the specific
the fluence of monoenergetic neutrons at a specific energy,
damage function is defined. See, for example,Annexes A1.2.2 Eref, required to produce the same displacement damage in a
and A2.2.2.
specified irradiated material, mat, as Φ(E).
3.1.1.1 Discussion—Observable changes in a material’s
3.1.4.1 Discussion—Note that Φ is equivalent to
eq,Eref,mat
properties attributable to the atomic displacement process are
Φ(E) if, and only if, the specific device effect (for example,
useful indices of displacement damage in that material. In current gain degradation in silicon) being correlated is de-
cases where the observed displacement damage is not in linear
scribed by the displacement damage function used in the
proportion to the applied fluence, the displacement damage calculation.
function represents the quotient d(observed damage)/dΦ in the
3.1.5 fluenceand fluence spectrum—see neutron fluenceand
limiting case of zero fluence. Examples of suitable represen-
neutron fluence spectrum.
tations of displacement damage functions are given in the
3.1.6 kerma factor—(K (E))the kermaperunitfluenceof
mat
annexes. In the case of silicon, damage mode of interest is the
particles of energy E present in a specified material, mat. See
change in minority-carrier recombination lifetime in the bulk
Terminology E170 for the definition of kerma, and a formula
semiconductor material. While several procedures exist to
for calculating the kerma factor.
directly measure the minority carrier lifetime in bulk material,
3.1.6.1 Discussion—When a material is irradiated by a
since this lifetime is related to the gain of a bipolar junction
neutron field, the energy imparted to charged particles in the
transistor(BJT),oneobservabledamagemetricistheBJTgain
material may be described by the kerma. The kerma may be
degradation. For this damage mode, it has been shown that the
divided into two parts, ionization kerma and displacement
displacement damage function may be successfully equated
kerma.See3.1.2.1forthedistinctionbetweenkermafactorand
with the microscopic displacement kerma factor.This question
microscopic kerma factor. Calculations of ionization and mi-
is discussed further in the annexes.
croscopic displacement kerma in silicon and gallium arsenide
3.1.2 microscopic displacement kerma factor—(κ (E))
D,mat
as a result of irradiation by neutrons with energies up to 20
the energy-dependent quotient of the displacement kerma per
MeV are described in Refs 5-8 and in the annexes.
targetatomandtheneutronfluence.κ (E)isproportionalto
D,mat
3.1.7 neutron fluenceand neutron fluence spectrumareused
K Ā/Φ, where K is the displacement kerma, Ā is the
D,mat D,mat
in this standard, and are special cases of fluence and fluence
spectrum as defined in E170.
3.1.7.1 Discussion—In cases where the context makes clear
Available from International Commission on Radiation Units and
that neutrons are referred to, the terms fluence and fluence
Measurements, 7910 Woodmont Avenue Suite 400 Bethesda, MD 20841-3095,
http://www.icru.org/ spectrum are sometimes used.
E722 − 19
4. Summary of Practice Thus, caution should be exercised in making a correlation
between calculated displacement damage and performance
4.1 The equivalent monoenergetic neutron fluence,
degradation of a given electronic device. The types of devices
Φ , is given as follows:
eq,Eref,mat
for which this correlation is applicable, and numerical evalu-
`
Φ E F E dE ation of displacement damage are discussed in the annexes.
* ~ ! ~ !
D,mat
Φ 5 (1)
eq,Eref,mat
F
5.3 Theconceptof1-MeVequivalentfluenceiswidelyused
D,Eref,mat
in the radiation-hardness testing community. It has merits and
where:
disadvantages that have been debated widely (9-12). For these
Φ(E) = incident neutron fluence spectrum,
reasons, specifics of a standard application of the 1-MeV
F (E) = neutron displacement damage function for the
D,mat
equivalent fluence are presented in the annexes.
irradiated material (displacement damage per
unit fluence) as a function of energy, and
6. Procedure for CalculatingΦ
eq,Eref,mat
F = displacement damage reference value desig-
D,Eref,mat
6.1 ToevaluateEq1and2,determinetheenergylimits E
min
nated for the irradiated material and for the
and E tobeusedinplaceofzeroandinfinityintheintegrals
max
specifiedequivalentenergy,Eref,asgiveninthe
of(Eq1)and(Eq2)andthevaluesofthedisplacementdamage
annexes.
function F (E) for the irradiated material and perform the
D,mat
The energy limits on the integral are determined in practice
indicated integrations.
by the incident neutron fluence spectrum and by the material
6.1.1 Choose the upper limit E to be at an energy above
max
being irradiated.
which the integral damage falls to an insignificant level. For
4.2 The neutron spectrum hardness parameter, H ,is Godiva- or TRIGA-type spectra, this limit is about 12 MeV.
Eref,mat
given as follows: 6.1.2 Choose the lower-energy limit E to be at an energy
min
belowwhichtheintegraldamagefallstoaninsignificantlevel.
`
Φ~E!F ~E!dE
*
D,mat
0 For silicon irradiated by Godiva-type spectra, this energy has
H 5 (2)
Eref,mat `
been historically chosen to be about 0.01 MeV. More highly
F Φ E dE
* ~ !
D,Eref,mat
moderated spectra may require lower thresholds or specialized
4.3 Oncetheneutronfluencespectrumhasbeendetermined
filtering requirements such as a boron shield, or both.
(for example, in accordance with Test Method E721) and the
6.1.3 The values of the neutron displacement damage func-
equivalent monoenergetic fluence calculated, then a monitor
tion used in Eq 1 and 2 obviously depend on the material and
(such as an activation foil) can be used in subsequent irradia-
the equivalent energy chosen. For silicon, resonance effects
tions at the same location to determine the fluence; that is, the
cause large variations (by a factor of 20 or more) in the
neutron fluence is then described in terms of the equivalent
displacementdamagefunctionasafunctionofenergyoverthe
monoenergetic neutron fluence per unit monitor response,
range from about 0.1 to 8 MeV (4, 5). Therefore, monoener-
Φ /M. Use of a monitor foil to predict Φ is
geticneutronsourceswiththeseenergiesmaynotbeusefulfor
eq,Eref,mat r eq,Eref,mat
valid only if the neutron spectrum remains constant.
effectstesting.Also,foraselectedequivalentenergy,thevalue
of F at that specific energy may not be representative
D,Eref,mat
5. Significance and Use
of the displacement damage function at nearby energies. In
such cases, a method of averaging the damage function over a
5.1 Thispracticeisimportantincharacterizingtheradiation
range of energies around the chosen equivalent energy can be
hardness of electronic devices irradiated by neutrons. This
used. Such averaging is discussed in the annexes. Because the
characterization makes it feasible to predict some changes in
F (E) term is normalized by dividing by F in Eq 1
operational properties of irradiated semiconductor devices or
D,mat D,Eref,mat
and2,onlytheshapeofthe F (E)functionversusenergyis
electronicsystems.Tofacilitateuniformityoftheinterpretation
D,mat
of primary importance. In such a case, precise knowledge of
and evaluation of results of irradiations by sources of different
the absolute values of F (E) is not required in evaluating
fluence spectra, it is convenient to reduce the incident neutron
D,mat
fluence from a source to a single parameter—an equivalent Φ and H .
eq,Eref,mat Eref,mat
monoenergetic neutron fluence—applicable to a particular
7. DeterminingΦ with a Monitor Foil
eq,Eref,mat
semiconductor material.
7.1 Atthesametimethatthefluencespectrum,Φ(E),ofthe
5.2 In order to determine an equivalent monoenergetic
sourceisdetermined(forexample,withanactivationfoilsetin
neutron fluence, it is necessary to evaluate the displacement
accordance with Guides E720 or E844, or both, and Test
damage of the particular semiconductor material. Ideally, this
Method E721 or Practice E944, or both) place a fast-neutron
quantityiscorrelatedtothedegradationofaspecificfunctional
monitor foil in the neutron field at an appropriate location.
performance parameter (such as current gain) of the semicon-
After Φ is determined and the monitor foil counted,
eq,Eref,mat
ductordeviceorsystembeingtested.However,thiscorrelation
calculate the ratio of the equivalent monoenergetic fluence to
hasnotbeenestablishedunequivocallyforalldevicetypesand
the unit monitor response, Φ /M.
eq,Eref,mat r
performance parameters since, in many instances, other effects
also can be important. Ionization effects produced by the 7.2 Use the response of the fast-neutron monitor foil, M,to
r
incident neutron fluence or by gamma rays in a mixed neutron predict Φ in subsequent routine device test irradia-
eq,Eref,mat
fluence, short-term and long-term annealing, and other factors tions. For this method to be valid, it is important to keep the
cancontributetoobservedperformancedegradation(damage). source-foil geometry essentially identical to that used for
E722 − 19
calibratingthemonitorfoil.Moderatechangesinsource-to-foil 8.1.2 Neutron source as to type and mode of operation
distance are allowable. In addition, make sure the source during tests (fast-pulse or steady state).
location (of a Godiva-type reactor) with respect to scattering
8.1.3 Neutron fluence spectrum and how it was determined.
materials (walls, floor, etc.) is the same. Do not change or
8.1.4 Monitor foil employed and the detector system used
move nearby scattering materials or moderators.
forcountingthefoil.Ifaneffectivefissioncrosssectionforthe
monitor foil is used, its value should be stated.
7.3 Precautions in maintaining original calibration condi-
tions are necessary to avoid altering the neutron fluence
8.1.5 The neutron displacement damage function should be
spectrum significantly in subsequent irradiations. An appre- given, or referenced. The specific material (for example,
ciable change in the spectrum will invalidate the calibration of
silicon) whose applicable damage function was used must be
the monitor foil and, therefore, would necessitate a new specified.ThevaluescitedinAnnexA1andAnnexA2shallbe
measurement of Φ(E) and recalibration of the monitor foil.
used for silicon and GaAs, respectively.
Whenever the neutron source configuration is changed, as for
8.1.6 Methods used for determining the average value of
example,ifthecorefuelelementsarereplacedorrearrangedin
F and the value of Eref selected. The values cited in
D,Eref,mat
a nuclear reactor, the activation foil spectrum measurements
Annex A1 and Annex A2 shall be used for silicon and GaAs,
and all quantities derived from them may need to be remea-
respectively.
sured.
8.1.7 Method used for evaluating the integrals of Eq 1 and
7.4 Thechoiceofamonitorfoilmaterialdependsonseveral 2 (for example, the energy bin width and number of bins in a
factors: numerical integration, and the limits of integration).
7.4.1 The activation threshold should be high enough so as
8.1.8 Values of Φ , H , and Φ /M.
eq,Eref,mat Eref,mat eq,Eref,mat r
to make it insensitive to neutrons below the E value used in
min
Eq 1 and 2. However, the threshold energy should be low
9. Precision and Bias
enough to sample a significant fraction of the total fluence.
9.1 TheprecisionincalculatingΦ andH will
eq,Eref,mat Eref,mat
7.4.2 The monitor foil should have a high neutron sensitiv-
dependonthemethodofevaluationoftheintegralsinEq1and
ity and a convenient half-life.
2 (for example, the width of the energy bins used in a
7.4.3 The detector system available for counting the moni-
numerical integration).
tor foil may dictate the choice of foil material. A germanium
54 58
gamma-ray detector system can be used, and Fe or Ni foils
9.2 The uncertainty of the calculated results depends on (1)
utilized as monitors. However, if a beta particle detector
knowledge of the neutron fluence spectrum, (2) knowledge of
system is available, then S foils are suitable. Details of the
the displacement damage functions over that energy spectrum,
use of sulfur foils are given in Test Method E265.
and (3) knowledge of the value of the average displacement
damage function at the specified equivalent energy.
8. Report
9.3 A specific example of the uncertainty associated with
8.1 In the report of the results of radiation-hardness tests in
the calculation of a 1-MeV equivalent fluence for silicon is
which an equivalent monoenergetic neutron fluence is
given in Annex A1.
calculated, the report should include at least the following
information:
10. Keywords
8.1.1 Semiconductor material and device performance pa-
rameter (for example, current gain in silicon bipolar transis- 10.1 displacement damage; electronic hardness; gallium
tors) degradation being correlated to displacement damage arsenide; hardness parameter; silicon; silicon damage; silicon
should be specified. equivalent damage (SED); 1–MeV equivalent fluence
ANNEXES
(Mandatory Information)
A1. CALCULATION OF 1-MeV EQUIVALENT NEUTRON FLUENCE FOR SILICON
A1.1 Background surface effect and is not within the scope of this standard. In
interpreting measurements of this 1-MeV(Si) damage, efforts
A1.1.1 The observable damage metric of interest in this
must be made to eliminate any interference from ionization-
annex is the change in gain of a silicon bipolar junction
related surface effects.
transistor (BJT) due to bulk displacement damage effects. The
damage mechanism is the change in minority-carrier recombi- A1.1.2 Thechoiceofthespecificenergyfordeterminingan
nation lifetime in the bulk semiconductor material. While a equivalent fluence has been the subject of some controversy
BJT gain may also be degraded by oxide traps and interface within the electronics hardness-testing community (9). Some
states introduced by the ionizing dose to the oxide, this is a workers (10) have proposed that 1 MeV be used while others
E722 − 19
(11, 12) have suggested 14 MeV to be more appropriate. The formalismofthepartitionfunction.Fig.A1.1showstheenergy
concept of 1-MeV equivalent fluence has gained broad accep- dependence of the silicon 1-MeV damage function.
tance in practice, and procedures for applying it to silicon are
A1.2.5 An average value of neutron microscopic displace-
described in this annex in some detail.
mentkermafactornear1MeVisdifficulttodeterminebecause
of sharp neutron cross-section resonances in that energy
A1.1.3 An important basis of the practice is the correlation
region. To avoid these difficulties, Namenson, Wolicki, and
ofradiationdamageeffectsinasemiconductordevicewiththe
Messenger (13) fitted the function A·E(1−exp(− B/E)) to
displacement kerma produced in bulk silicon by neutron
varioustabulationsofκ (E)versusenergy.ThevaluesofAand
irradiation. This correlation assumes that volume (versus
D
B obtained by a least squares fit yielded an average value at 1
surface)effectsarethedominantradiationdamagemechanism.
MeVof95 64MeV·mbarn.Asimilarprocedureappliedtothe
Experimental evidence indicates that displacement kerma is a
valid measure of device performance degradation (for data given in Table A1.1 also gives a value close to 95
MeV·mbarn (22). Accordingly, the designated value of F
example,reductionincurrentgain)inbipolartransistorswhose
D,
operation basically depends on volume mechanisms (13, 14). 1MeV,SitobeusedinEq1and2tocalculatea1-MeVequivalent
fluence is 95 MeV·mbarn.
However, for device types governed by surface phenomena
(such as MOSFET devices), it is clear that this correlation is
A1.2.6 For purposes of intercomparison of hardness testing
not valid. Surface-effect devices are more sensitive than are
resultsfromvariouslaboratories,thevalueofF usedin
D,1MeV,Si
volume-effect devices to ionization radiation effects produced
obtainingsuchresultsisveryimportant;therefore,reportingof
either by a neutron field or a mixed neutron-gamma field.
results should include confirmation that the value of F
D,1MeV,Si
Therefore, the basic mechanism associated with device perfor-
designated in A1.2.5 was used in any calculation.
mance and the effect being correlated (for example, gain
A1.2.7 Once the neutron fluence spectrum Φ(E) has been
degradation) should be kept in mind before applying this
determinedfortheenergyrangeofinterest,thenusenumerical
practice at any equivalent energy.
integrationtoevaluateEq1and2,usingvaluesfor F (E)from
D
Table A1.1 and F =95 MeV·mbarn.
A1.2 Calculation ofΦ
D,1MeV,Si
eq,1MeV,Si
A1.2.1 The displacement damage function, F (E), de-
D,mat A1.3 Precision and Bias
fined for silicon in this annex is the silicon microscopic
A1.3.1 The values for κ (E) given in Table A1.1 are
D,Si
displacement kerma factor, as tabulated in Table A1.1.
determined by calculating the total displacement kerma using
A1.2.2 A1-MeVequivalent fluence in silicon is defined for
the methodology implemented in the NJOY-2012 code (18),
an irradiation by neutrons of any neutron spectrum for which
and then partitioning it into ionization and displacement
the predominant source of displacement damage is from
fractions using the Robinson partition function (17). Because
neutrons of energy between 10 keV and 20 MeV. The neutron
of the lack of adequate theory to perform the partition of the
fluencespectrum,Φ(E),maybethatdeterminedfromaneutron
kerma and due to the uncertainties in cross sections, the
transport calculation, that determined from measurements, or
estimated uncertainty in the microscopic displacement kerma
that given in an environment specification document.
factor is about 10% up to 3 MeV (22, 23). Correlation of the
microscopic displacement kerma with measured damage in
A1.2.3 The neutron fluence spectrum, Φ(E), may be deter-
many neutron fields has been confirmed with uncertainties no
minedexperimentallybymeasuringasetofactivationfoilsand
larger than 10% (14).
thenbyapplicationofaspectraladjustmentcomputercode(see
Guide E720 and Test Method E721 for details).
A1.3.2 Uncertaintiesintheneutronfluencespectrum,Φ(E),
will vary based on the method used to obtain it. If neutron
A1.2.4 Results of calculations of silicon microscopic dis-
sensors such as activation foils were used, see Standard Guide
placement kerma factors (displacement kerma per target atom
E721.
per unit neutron fluence), κ (E), are given in Table A1.1 as
D,Si
−10
a function of neutron energy over the range from 10 to 20 A1.3.3 SincethismandatoryannexrequirestheuseofTable
MeV (15). The unit of the microscopic kerma factor is A1.1 and F =95 MeV·mbarn, no uncertainty in the
D,1MeV,Si
megaelectron volt times millibarns (MeV·mbarn). Each factor calculation of 1-MeV equivalent fluence is attributable to the
−13 2
canbemultipliedby3.435×10 toconverttorad(Si)·cm,or consistent use of these data. Therefore only the uncertainty in
−19 2 2
by 3.435×10 to convert to J·m /kg or Gy(Si)·m . The the determination of Φ(E) need be considered in assigning an
silicon microscopic displacement kerma factor as given in uncertaintytothe1-MeVequivalentfluence.Anuncertaintyin
TableA1.1 is the accepted silicon damage function to be used the spectrum in the range 620%, would most often lead to
in the application of this standard: F ~E!5κ ~E!. This uncertainties no more than 610% in the integral quantity
D,Si D,Si
microscopic displacement kerma was computed by using the Φ . While no specific group structure for representing
eq,1MeV,Si
28 29 30
ENDF/B-VIII.0 cross sections (16) for Si, Si and Si in the neutron fluence spectrum is recommended, the choice of
their natural abundance composition shown in TableA1.2, the energy bin boundaries will affect the uncertainty in the 1-MeV
RobinsonfittotheLindhardenergypartitionfunction (17),and equivalent fluence. The energy bin boundaries should be
the NJOY-2012 processing code (18). The elemental silicon chosenwithdueconsiderationfortheshapeofboththeneutron
atomic weight of 28.085 amu is used for the elemental silicon spectrum and the 1-MeV equivalent damage function. A poor
lattice atom atomic weight (19) and it is converted from amu choice of the energy group structure used to evaluate the
into neutron mass units before it is used in the Robinson integral in Eq 2 could increase this uncertainty (see 8.1.7).
E722 − 19
nat
TABLE A1.1 Silicon Damage Function
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
1 2.000000E+01 1.995000E+01 1.973868E+02
2 1.990000E+01 1.985000E+01 1.967664E+02
3 1.980000E+01 1.975000E+01 1.961368E+02
4 1.970000E+01 1.965000E+01 1.955665E+02
5 1.960000E+01 1.955000E+01 1.952573E+02
6 1.950000E+01 1.945000E+01 1.950075E+02
7 1.940000E+01 1.935000E+01 1.949787E+02
8 1.930000E+01 1.925000E+01 1.951091E+02
9 1.920000E+01 1.915000E+01 1.955607E+02
10 1.910000E+01 1.905000E+01 1.968811E+02
11 1.900000E+01 1.895000E+01 1.981732E+02
12 1.890000E+01 1.885000E+01 1.991148E+02
13 1.880000E+01 1.875000E+01 1.999262E+02
14 1.870000E+01 1.865000E+01 1.977638E+02
15 1.860000E+01 1.855000E+01 1.938703E+02
16 1.850000E+01 1.845000E+01 1.920284E+02
17 1.840000E+01 1.835000E+01 1.930398E+02
18 1.830000E+01 1.825000E+01 1.941703E+02
19 1.820000E+01 1.815000E+01 1.955830E+02
20 1.810000E+01 1.805000E+01 1.963928E+02
21 1.800000E+01 1.795000E+01 1.941498E+02
22 1.790000E+01 1.785000E+01 1.916968E+02
23 1.780000E+01 1.775000E+01 1.904943E+02
24 1.770000E+01 1.765000E+01 1.897224E+02
25 1.760000E+01 1.755000E+01 1.907523E+02
26 1.750000E+01 1.745000E+01 1.921376E+02
27 1.740000E+01 1.735000E+01 1.923461E+02
28 1.730000E+01 1.725000E+01 1.922046E+02
29 1.720000E+01 1.715000E+01 1.924038E+02
30 1.710000E+01 1.705000E+01 1.926536E+02
31 1.700000E+01 1.695000E+01 1.920722E+02
32 1.690000E+01 1.685000E+01 1.915217E+02
33 1.680000E+01 1.675000E+01 1.936340E+02
34 1.670000E+01 1.665000E+01 1.952966E+02
35 1.660000E+01 1.655000E+01 1.902622E+02
36 1.650000E+01 1.645000E+01 1.856090E+02
37 1.640000E+01 1.635000E+01 1.865312E+02
38 1.630000E+01 1.625000E+01 1.877142E+02
39 1.620000E+01 1.615000E+01 1.882977E+02
40 1.610000E+01 1.605000E+01 1.882490E+02
41 1.600000E+01 1.595000E+01 1.874403E+02
42 1.590000E+01 1.585000E+01 1.842194E+02
43 1.580000E+01 1.575000E+01 1.802182E+02
44 1.570000E+01 1.565000E+01 1.791307E+02
45 1.560000E+01 1.555000E+01 1.792942E+02
46 1.550000E+01 1.545000E+01 1.811301E+02
47 1.540000E+01 1.535000E+01 1.822846E+02
48 1.530000E+01 1.525000E+01 1.823885E+02
49 1.520000E+01 1.515000E+01 1.783886E+02
50 1.510000E+01 1.505000E+01 1.756900E+02
51 1.500000E+01 1.495000E+01 1.794274E+02
52 1.490000E+01 1.485000E+01 1.788293E+02
53 1.480000E+01 1.475000E+01 1.755598E+02
54 1.470000E+01 1.465000E+01 1.746830E+02
55 1.460000E+01 1.455000E+01 1.770211E+02
56 1.450000E+01 1.445000E+01 1.821349E+02
57 1.440000E+01 1.435000E+01 1.819542E+02
58 1.430000E+01 1.425000E+01 1.807217E+02
59 1.420000E+01 1.415000E+01 1.794793E+02
60 1.410000E+01 1.405000E+01 1.765542E+02
61 1.400000E+01 1.395000E+01 1.785629E+02
62 1.390000E+01 1.385000E+01 1.844297E+02
63 1.380000E+01 1.375000E+01 1.781225E+02
64 1.370000E+01 1.365000E+01 1.757290E+02
65 1.360000E+01 1.355000E+01 1.778709E+02
66 1.350000E+01 1.345000E+01 1.813241E+02
67 1.340000E+01 1.335000E+01 1.781406E+02
68 1.330000E+01 1.325000E+01 1.768893E+02
69 1.320000E+01 1.315000E+01 1.801226E+02
70 1.310000E+01 1.305000E+01 1.832955E+02
71 1.300000E+01 1.295000E+01 1.824153E+02
72 1.290000E+01 1.285000E+01 1.820566E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
73 1.280000E+01 1.275000E+01 1.826390E+02
74 1.270000E+01 1.265000E+01 1.807486E+02
75 1.260000E+01 1.255000E+01 1.731323E+02
76 1.250000E+01 1.245000E+01 1.762513E+02
77 1.240000E+01 1.235000E+01 1.792074E+02
78 1.230000E+01 1.225000E+01 1.785140E+02
79 1.220000E+01 1.215000E+01 1.781711E+02
80 1.210000E+01 1.205000E+01 1.754457E+02
81 1.200000E+01 1.195000E+01 1.737800E+02
82 1.190000E+01 1.185000E+01 1.724747E+02
83 1.180000E+01 1.175000E+01 1.721396E+02
84 1.170000E+01 1.165000E+01 1.736148E+02
85 1.160000E+01 1.155000E+01 1.746005E+02
86 1.150000E+01 1.145000E+01 1.733552E+02
87 1.140000E+01 1.135000E+01 1.703988E+02
88 1.130000E+01 1.125000E+01 1.662376E+02
89 1.120000E+01 1.115000E+01 1.650580E+02
90 1.110000E+01 1.105000E+01 1.702935E+02
91 1.100000E+01 1.095000E+01 1.729656E+02
92 1.090000E+01 1.085000E+01 1.730395E+02
93 1.080000E+01 1.075000E+01 1.692476E+02
94 1.070000E+01 1.065000E+01 1.643638E+02
95 1.060000E+01 1.055000E+01 1.664527E+02
96 1.050000E+01 1.045000E+01 1.676141E+02
97 1.040000E+01 1.035000E+01 1.736229E+02
98 1.030000E+01 1.025000E+01 1.728499E+02
99 1.020000E+01 1.015000E+01 1.744761E+02
100 1.010000E+01 1.005000E+01 1.723774E+02
101 1.000000E+01 9.950000E+00 1.741678E+02
102 9.900000E+00 9.850000E+00 1.717298E+02
103 9.800000E+00 9.750000E+00 1.672486E+02
104 9.700000E+00 9.650000E+00 1.636157E+02
105 9.600000E+00 9.550000E+00 1.729551E+02
106 9.500000E+00 9.450000E+00 1.782361E+02
107 9.400000E+00 9.350000E+00 1.711540E+02
108 9.300000E+00 9.250000E+00 1.578282E+02
109 9.200000E+00 9.150000E+00 1.635106E+02
110 9.100000E+00 9.050000E+00 1.831674E+02
111 9.000000E+00 8.950000E+00 1.835292E+02
112 8.900000E+00 8.850000E+00 1.641407E+02
113 8.800000E+00 8.750000E+00 1.536291E+02
114 8.700000E+00 8.650000E+00 1.711415E+02
115 8.600000E+00 8.550000E+00 1.718448E+02
116 8.500000E+00 8.450000E+00 1.729498E+02
117 8.400000E+00 8.350000E+00 1.717610E+02
118 8.300000E+00 8.250000E+00 1.693958E+02
119 8.200000E+00 8.150000E+00 1.622010E+02
120 8.100000E+00 8.050000E+00 1.768217E+02
121 8.000000E+00 7.950000E+00 1.942243E+02
122 7.900000E+00 7.850000E+00 1.809926E+02
123 7.800000E+00 7.750000E+00 1.810599E+02
124 7.700000E+00 7.650000E+00 1.741924E+02
125 7.600000E+00 7.550000E+00 1.713542E+02
126 7.500000E+00 7.450000E+00 1.742301E+02
127 7.400000E+00 7.350000E+00 1.763690E+02
128 7.300000E+00 7.250000E+00 1.754672E+02
129 7.200000E+00 7.150000E+00 1.429532E+02
130 7.100000E+00 7.050000E+00 1.727034E+02
131 7.000000E+00 6.950000E+00 1.475553E+02
132 6.900000E+00 6.850000E+00 1.528027E+02
133 6.800000E+00 6.750000E+00 1.727339E+02
134 6.700000E+00 6.650000E+00 1.566315E+02
135 6.600000E+00 6.550000E+00 1.281781E+02
136 6.500000E+00 6.450000E+00 1.469991E+02
137 6.400000E+00 6.350000E+00 1.590746E+02
138 6.300000E+00 6.250000E+00 1.835404E+02
139 6.200000E+00 6.150000E+00 1.321562E+02
140 6.100000E+00 6.050000E+00 1.611566E+02
141 6.000000E+00 5.950000E+00 1.421075E+02
142 5.900000E+00 5.850000E+00 1.733649E+02
143 5.800000E+00 5.750000E+00 1.868717E+02
144 5.700000E+00 5.650000E+00 1.559314E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
145 5.600000E+00 5.550000E+00 1.514860E+02
146 5.500000E+00 5.450000E+00 1.234471E+02
147 5.400000E+00 5.350000E+00 1.290942E+02
148 5.300000E+00 5.250000E+00 1.551565E+02
149 5.200000E+00 5.150000E+00 1.765639E+02
150 5.100000E+00 5.050000E+00 1.551267E+02
151 5.000000E+00 4.950000E+00 1.516193E+02
152 4.900000E+00 4.850000E+00 1.651634E+02
153 4.800000E+00 4.750000E+00 1.927708E+02
154 4.700000E+00 4.650000E+00 1.608431E+02
155 4.600000E+00 4.550000E+00 1.439489E+02
156 4.500000E+00 4.450000E+00 1.447625E+02
157 4.400000E+00 4.350000E+00 1.385367E+02
158 4.300000E+00 4.250000E+00 1.710236E+02
159 4.200000E+00 4.150000E+00 1.101688E+02
160 4.100000E+00 4.050000E+00 1.370340E+02
161 4.000000E+00 3.950000E+00 1.392049E+02
162 3.900000E+00 3.850000E+00 1.138522E+02
163 3.800000E+00 3.750000E+00 1.184181E+02
164 3.700000E+00 3.650000E+00 7.169035E+01
165 3.600000E+00 3.550000E+00 1.160873E+02
166 3.500000E+00 3.450000E+00 1.203618E+02
167 3.400000E+00 3.350000E+00 1.166044E+02
168 3.300000E+00 3.250000E+00 1.228177E+02
169 3.200000E+00 3.150000E+00 1.364921E+02
170 3.100000E+00 3.050000E+00 1.219693E+02
171 3.000000E+00 2.950000E+00 1.012464E+02
172 2.900000E+00 2.850000E+00 1.373463E+02
173 2.800000E+00 2.750000E+00 1.099198E+02
174 2.700000E+00 2.650000E+00 1.178785E+02
175 2.600000E+00 2.550000E+00 1.317324E+02
176 2.500000E+00 2.450000E+00 1.207865E+02
177 2.400000E+00 2.350000E+00 1.053801E+02
178 2.300000E+00 2.250000E+00 1.072764E+02
179 2.200000E+00 2.150000E+00 1.102115E+02
180 2.100000E+00 2.050000E+00 9.719414E+01
181 2.000000E+00 1.950000E+00 1.323761E+02
182 1.900000E+00 1.850000E+00 1.340592E+02
183 1.800000E+00 1.750000E+00 7.996942E+01
184 1.700000E+00 1.650000E+00 1.688371E+02
185 1.600000E+00 1.550000E+00 1.084512E+02
186 1.500000E+00 1.450000E+00 1.030271E+02
187 1.400000E+00 1.350000E+00 9.005495E+01
188 1.300000E+00 1.250000E+00 9.234239E+01
189 1.200000E+00 1.150000E+00 6.350020E+01
190 1.100000E+00 1.050000E+00 7.729120E+01
191 1.000000E+00 9.800000E-01 1.122903E+02
192 9.600000E-01 9.400000E-01 1.117714E+02
193 9.200000E-01 9.000000E-01 9.082997E+01
194 8.800000E-01 8.600000E-01 8.005856E+01
195 8.400000E-01 8.200000E-01 1.396158E+02
196 8.000000E-01 7.800000E-01 8.899613E+01
197 7.600000E-01 7.400000E-01 6.515221E+01
198 7.200000E-01 7.050000E-01 5.826901E+01
199 6.900000E-01 6.750000E-01 5.601357E+01
200 6.600000E-01 6.450000E-01 5.471756E+01
201 6.300000E-01 6.150000E-01 5.308440E+01
202 6.000000E-01 5.875000E-01 5.825823E+01
203 5.750000E-01 5.625000E-01 1.231737E+02
204 5.500000E-01 5.375000E-01 7.357404E+01
205 5.250000E-01 5.125000E-01 5.831835E+01
206 5.000000E-01 4.875000E-01 5.577959E+01
207 4.750000E-01 4.625000E-01 5.420316E+01
208 4.500000E-01 4.375000E-01 5.295185E+01
209 4.250000E-01 4.125000E-01 5.247011E+01
210 4.000000E-01 3.900000E-01 5.165452E+01
211 3.800000E-01 3.700000E-01 4.895189E+01
212 3.600000E-01 3.500000E-01 4.953166E+01
213 3.400000E-01 3.300000E-01 5.046942E+01
214 3.200000E-01 3.100000E-01 5.080648E+01
215 3.000000E-01 2.900000E-01 5.231158E+01
216 2.800000E-01 2.750000E-01 5.374312E+01
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
217 2.700000E-01 2.625000E-01 5.592848E+01
218 2.550000E-01 2.475000E-01 5.962491E+01
219 2.400000E-01 2.350000E-01 6.471726E+01
220 2.300000E-01 2.250000E-01 7.066167E+01
221 2.200000E-01 2.150000E-01 7.958649E+01
222 2.100000E-01 2.050000E-01 9.289946E+01
223 2.000000E-01 1.950000E-01 1.103763E+02
224 1.900000E-01 1.850000E-01 1.135182E+02
225 1.800000E-01 1.750000E-01 6.619505E+01
226 1.700000E-01 1.650000E-01 2.035817E+01
227 1.600000E-01 1.550000E-01 4.399004E+00
228 1.500000E-01 1.462500E-01 1.020993E+00
229 1.425000E-01 1.387500E-01 1.181040E+00
230 1.350000E-01 1.312500E-01 1.911953E+00
231 1.275000E-01 1.237500E-01 2.718806E+00
232 1.200000E-01 1.175000E-01 3.362332E+00
233 1.150000E-01 1.125000E-01 3.810700E+00
234 1.100000E-01 1.075000E-01 4.218445E+00
235 1.050000E-01 1.025000E-01 4.562947E+00
236 1.000000E-01 9.800000E-02 4.841910E+00
237 9.600000E-02 9.400000E-02 5.043317E+00
238 9.200000E-02 9.000000E-02 5.218990E+00
239 8.800000E-02 8.600000E-02 5.394066E+00
240 8.400000E-02 8.200000E-02 5.506921E+00
241 8.000000E-02 7.800000E-02 5.642253E+00
242 7.600000E-02 7.400000E-02 5.797199E+00
243 7.200000E-02 7.050000E-02 5.975362E+00
244 6.900000E-02 6.750000E-02 6.420804E+00
245 6.600000E-02 6.450000E-02 6.693609E+00
246 6.300000E-02 6.150001E-02 7.737466E+00
247 6.000000E-02 5.875000E-02 1.126351E+01
248 5.750000E-02 5.625000E-02 4.847429E+01
249 5.500000E-02 5.375000E-02 1.400141E+00
250 5.250000E-02 5.125000E-02 1.662603E+00
251 5.000000E-02 4.875000E-02 2.315137E+00
252 4.750000E-02 4.625000E-02 2.613727E+00
253 4.500000E-02 4.375000E-02 2.750118E+00
254 4.250000E-02 4.125000E-02 2.795498E+00
255 4.000000E-02 3.900000E-02 3.225666E+00
256 3.800000E-02 3.700000E-02 2.747026E+00
257 3.600000E-02 3.500000E-02 2.683286E+00
258 3.400000E-02 3.300000E-02 2.604141E+00
259 3.200000E-02 3.100000E-02 2.513165E+00
260 3.000000E-02 2.900000E-02 2.405056E+00
261 2.800000E-02 2.750000E-02 2.312229E+00
262 2.700000E-02 2.625000E-02 2.230672E+00
263 2.550000E-02 2.475000E-02 2.132857E+00
264 2.400000E-02 2.350000E-02 2.051692E+00
265 2.300000E-02 2.250000E-02 1.986533E+00
266 2.200000E-02 2.150000E-02 1.921226E+00
267 2.100000E-02 2.050000E-02 1.855926E+00
268 2.000000E-02 1.950000E-02 1.785253E+00
269 1.900000E-02 1.850000E-02 1.709402E+00
270 1.800000E-02 1.750000E-02 1.632872E+00
271 1.700000E-02 1.650000E-02 1.553278E+00
272 1.600000E-02 1.550000E-02 1.550785E+00
273 1.500000E-02 1.462500E-02 1.401943E+00
274 1.425000E-02 1.387500E-02 1.338281E+00
275 1.350000E-02 1.312500E-02 1.274953E+00
276 1.275000E-02 1.237500E-02 1.211063E+00
277 1.200000E-02 1.175000E-02 1.156115E+00
278 1.150000E-02 1.125000E-02 1.111962E+00
279 1.100000E-02 1.075000E-02 1.067720E+00
280 1.050000E-02 1.025000E-02 1.023548E+00
281 1.000000E-02 9.800000E-03 9.832039E-01
282 9.600000E-03 9.400000E-03 9.466112E-01
283 9.200000E-03 9.000000E-03 9.100199E-01
284 8.800000E-03 8.600000E-03 8.731043E-01
285 8.400000E-03 8.200000E-03 8.356686E-01
286 8.000000E-03 7.800000E-03 7.982407E-01
287 7.600000E-03 7.400000E-03 7.605540E-01
288 7.200000E-03 7.050000E-03 7.271539E-01
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
289 6.900000E-03 6.750000E-03 6.984250E-01
290 6.600000E-03 6.450000E-03 6.697010E-01
291 6.300000E-03 6.150000E-03 6.407355E-01
292 6.000000E-03 5.875000E-03 6.138325E-01
293 5.750000E-03 5.625000E-03 5.893337E-01
294 5.500000E-03 5.375000E-03 5.648403E-01
295 5.250000E-03 5.125000E-03 5.406927E-01
296 5.000000E-03 4.875000E-03 5.465844E-01
297 4.750000E-03 4.625000E-03 4.905972E-01
298 4.500000E-03 4.375000E-03 4.655979E-01
299 4.250000E-03 4.125000E-03 4.404136E-01
300 4.000000E-03 3.900000E-03 4.176310E-01
301 3.800000E-03 3.700000E-03 3.973314E-01
302 3.600000E-03 3.500000E-03 3.769914E-01
303 3.400000E-03 3.300000E-03 3.564086E-01
304 3.200000E-03 3.100000E-03 3.357770E-01
305 3.000000E-03 2.900000E-03 3.151550E-01
306 2.800000E-03 2.750000E-03 2.997556E-01
307 2.700000E-03 2.625000E-03 2.866856E-01
308 2.550000E-03 2.475000E-03 2.710611E-01
309 2.400000E-03 2.350000E-03 2.583126E-01
310 2.300000E-03 2.250000E-03 4.309242E-01
311 2.200000E-03 2.150000E-03 2.375994E-01
312 2.100000E-03 2.050000E-03 2.263939E-01
313 2.000000E-03 1.950000E-03 2.157340E-01
314 1.900000E-03 1.850000E-03 2.050798E-01
315 1.800000E-03 1.750000E-03 1.944260E-01
316 1.700000E-03 1.650000E-03 1.837176E-01
317 1.600000E-03 1.550000E-03 1.730096E-01
318 1.500000E-03 1.462500E-03 1.636211E-01
319 1.425000E-03 1.387500E-03 1.555293E-01
320 1.350000E-03 1.312500E-03 1.474280E-01
321 1.275000E-03 1.237500E-03 1.393159E-01
322 1.200000E-03 1.175000E-03 1.325419E-01
323 1.150000E-03 1.125000E-03 1.271045E-01
324 1.100000E-03 1.075000E-03 1.216567E-01
325 1.050000E-03 1.025000E-03 1.162187E-01
326 1.000000E-03 9.800000E-04 1.113118E-01
327 9.600000E-04 9.400000E-04 1.069259E-01
328 9.200000E-04 9.000000E-04 1.025398E-01
329 8.800000E-04 8.600000E-04 9.815125E-02
330 8.400000E-04 8.200000E-04 9.374607E-02
331 8.000000E-04 7.800000E-04 8.934105E-02
332 7.600000E-04 7.400000E-04 8.492854E-02
333 7.200000E-04 7.050000E-04 8.106306E-02
334 6.900000E-04 6.750000E-04 7.774240E-02
335 6.600000E-04 6.450000E-04 7.442159E-02
336 6.300000E-04 6.150000E-04 7.109369E-02
337 6.000000E-04 5.875000E-04 6.803714E-02
338 5.750000E-04 5.625000E-04 6.525391E-02
339 5.500000E-04 5.375000E-04 6.247165E-02
340 5.250000E-04 5.125000E-04 5.968847E-02
341 5.000000E-04 4.875000E-04 5.689916E-02
342 4.750000E-04 4.625000E-04 5.410275E-02
343 4.500000E-04 4.375000E-04 5.130730E-02
344 4.250000E-04 4.125000E-04 4.850670E-02
345 4.000000E-04 3.900000E-04 4.598757E-02
346 3.800000E-04 3.700000E-04 4.374376E-02
347 3.600000E-04 3.500000E-04 4.149899E-02
348 3.400000E-04 3.300000E-04 3.924896E-02
349 3.200000E-04 3.100000E-04 3.699887E-02
350 3.000000E-04 2.900000E-04 3.474781E-02
351 2.800000E-04 2.750000E-04 3.306993E-02
352 2.700000E-04 2.625000E-04 3.165800E-02
353 2.550000E-04 2.475000E-04 2.996848E-02
354 2.400000E-04 2.350000E-04 2.856477E-02
355 2.300000E-04 2.250000E-04 2.743848E-02
356 2.200000E-04 2.150000E-04 2.631218E-02
357 2.100000E-04 2.050000E-04 2.518586E-02
358 2.000000E-04 1.950000E-04 2.406039E-02
359 1.900000E-04 1.850000E-04 2.293579E-02
360 1.800000E-04 1.750000E-04 2.181216E-02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
361 1.700000E-04 1.650000E-04 2.069035E-02
362 1.600000E-04 1.550000E-04 1.956859E-02
363 1.500000E-04 1.462500E-04 1.859254E-02
364 1.425000E-04 1.387500E-04 1.775523E-02
365 1.350000E-04 1.312500E-04 1.691889E-02
366 1.275000E-04 1.237500E-04 1.608444E-02
367 1.200000E-04 1.175000E-04 1.539672E-02
368 1.150000E-04 1.125000E-04 1.484494E-02
369 1.10000
...

This document is not an ASTM standard and is intended only to provide the user of an ASTM standard an indication of what changes have been made to the previous version. Because
it may not be technically possible to adequately depict all changes accurately, ASTM recommends that users consult prior editions as appropriate. In all cases only the current version
of the standard as published by ASTM is to be considered the official document.
Designation: E722 − 14 E722 − 19
Standard Practice for
Characterizing Neutron Fluence Spectra in Terms of an
Equivalent Monoenergetic Neutron Fluence for Radiation-
Hardness Testing of Electronics
This standard is issued under the fixed designation E722; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
This standard has been approved for use by agencies of the U.S. Department of Defense.
1. Scope
1.1 This practice covers procedures for characterizing neutron fluence from a source in terms of an equivalent monoenergetic
neutron fluence. It is applicable to neutron effects testing, to the development of test specifications, and to the characterization of
neutron test environments. The sources may have a broad neutron-energy range, or may be mono-energetic neutron sources with
energies up to 20 MeV. This practice is not applicable in cases where the predominant source of displacement damage is from
neutrons of energy less than 10 keV. The relevant equivalence is in terms of a specified effect on certain physical properties of
materials upon which the source spectrum is incident. In order to achieve this, knowledge of the effects of neutrons as a function
of energy on the specific property of the material of interest is required. Sharp variations in the effects with neutron energy may
limit the usefulness of this practice in the case of mono-energetic sources.
1.2 This practice is presented in a manner to be of general application to a variety of materials and sources. Correlation between
displacements (1-3) caused by different particles (electrons, neutrons, protons, and heavy ions) is beyond out of the scope of this
practice. practice but is addressed in Practice E3084. In radiation-hardness testing of electronic semiconductor devices, specific
materials of interest include silicon and gallium arsenide, and the neutron sources generally are test and research reactors and
californium-252 irradiators.
1.3 The technique involved relies on the following factors: (1) a detailed determination of the fluence spectrum of the neutron
source, and (2) a knowledge of the degradation (damage) effects of neutrons as a function of energy on specific material properties.
1.4 The detailed determination of the neutron fluence spectrum referred to in 1.3 need not be performed afresh for each test
exposure, provided the exposure conditions are repeatable. When the spectrum determination is not repeated, a neutron fluence
monitor shall be used for each test exposure.
1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard,
2 2
except for MeV, keV, eV, MeV·mbarn, rad(Si)·cm , and rad(GaAs)·cm .
1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility
of the user of this standard to establish appropriate safety safety, health, and healthenvironmental practices and determine the
applicability of regulatory limitations prior to use.
1.7 This international standard was developed in accordance with internationally recognized principles on standardization
established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued
by the World Trade Organization Technical Barriers to Trade (TBT) Committee.
2. Referenced Documents
2.1 ASTM Standards:
E170 Terminology Relating to Radiation Measurements and Dosimetry
E265 Test Method for Measuring Reaction Rates and Fast-Neutron Fluences by Radioactivation of Sulfur-32
This practice is under the jurisdiction of ASTM Committee E10 on Nuclear Technology and Applicationsand is the direct responsibility of Subcommittee E10.07 on
Radiation Dosimetry for Radiation Effects on Materials and Devices.
Current edition approved June 1, 2014Oct. 1, 2019. Published October 2014October 2019. Originally approved in 1980. Last previous edition approved in 20092014 as
ε1
E722 – 09E722 – 14. . DOI: 10.1520/E0722-14.10.1520/E0722-19.
The boldface numbers in parentheses refer to a list of references at the end of this practice.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or contact ASTM Customer Service at [e-mail]. For Annual Book of ASTM Standards
volume information, refer to the standard’s Document Summary page on the ASTM website.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
E722 − 19
E693 Practice for Characterizing Neutron Exposures in Iron and Low Alloy Steels in Terms of Displacements Per Atom (DPA)
E720 Guide for Selection and Use of Neutron Sensors for Determining Neutron Spectra Employed in Radiation-Hardness
Testing of Electronics
E721 Guide for Determining Neutron Energy Spectra from Neutron Sensors for Radiation-Hardness Testing of Electronics
E844 Guide for Sensor Set Design and Irradiation for Reactor Surveillance
E944 Guide for Application of Neutron Spectrum Adjustment Methods in Reactor Surveillance
E3084 Practice for Characterizing Particle Irradiations of Materials in Terms of Non-Ionizing Energy Loss (NIEL)
2.2 International Commission on Radiation Units and Measurements (ICRU) Reports:
ICRU Report 13 Neutron Fluence, Neutron Spectra, and Kerma
ICRU Report 60 Fundamental Quantities and Units for Ionizing Radiation
ICRU Report 85 Fundamental Quantities and Units for Ionizing Radiation (Revised)
3. Terminology
3.1 Definitions of Terms Specific to This Standard:
3.1.1 displacement damage function—(F (E)) an energy-dependent parameter proportional to the quotient of the observable
D,mat
displacement damage per target atom and the neutron fluence. Different displacement-related damage functions may exist, so the
damage mode of interest and the observation procedure shall be identified when the specific damage function is defined. See, for
example, Annexes A1.2.2 and A2.2.2.
3.1.1.1 Discussion—
Observable changes in a material’s properties attributable to the atomic displacement process are useful indices of displacement
damage in that material. In cases where the observed displacement damage is not in linear proportion to the applied fluence, the
displacement damage function represents the quotient d(observed damage)/dΦ in the limiting case of zero fluence. Examples of
suitable representations of displacement damage functions are given in the annexes. In the case of silicon, damage mode of interest
is the change in minority-carrier recombination lifetime in the bulk semiconductor material. While several procedures exist to
directly measure the minority carrier lifetime in bulk material, since this lifetime is related to the gain of a bipolar junction
transistor (BJT), one observable damage metric is the BJT gain degradation. For this damage mode, it has been shown that the
displacement damage function may be successfully equated with the microscopic displacement kerma factor. This question is
discussed further in the annexes.
3.1.2 microscopic displacement kerma factor—(κ (E)) the energy-dependent quotient of the displacement kerma per target
D,mat
atom and the neutron fluence. κ (E) is proportional to K Ā/Φ, where K is the displacement kerma, Ā is the mean atomic
D,mat D,mat D,mat
mass of the material and Φ is the neutron fluence from a monoenergetic source of energy E.
3.1.2.1 Discussion—
This quantity may be calculated from the microscopic neutron interaction cross sections, the kinematic relations for each reaction
and from a suitable partition function which divides the total kerma into ionization and displacement kerma. The use of the term
microscopic kerma factor in this standard is to indicate that energy times area per atom is used, instead of per unit mass, as in the
term kerma factor defined in E170.
3.1.3 fluence spectrum hardness parameter—(H = Φ /Φ) this parameter is defined as the ratio of the equivalent
Eref,mat eq,Eref,mat
monoenergetic neutron fluence to the total fluence, Φ /Φ. The numerical value of the hardness parameter is also equal to
eq,Eref,mat
the fluence of monoenergetic neutrons at the specific energy, Eref, required to produce the same displacement damage in the
specified material, mat, as unit fluence of neutrons of neutron spectrum Φ(E).
3.1.3.1 Discussion—
For damage correlation, a convenient method of characterizing the shape of an incident neutron fluence spectrum Φ(E), is in terms
of a fluence spectrum hardness parameter (4). The hardness parameter in a particular neutron field depends on the displacement
damage function used to compute the damage (see annexes) and is therefore different for different semiconductor materials.
3.1.4 equivalent monoenergetic neutron fluence—(Φ ) an equivalent monoenergetic neutron fluence, Φ ,
eq,Eref,mat eq,Eref,mat
characterizes an incident fluence spectrum, Φ(E), in terms of the fluence of monoenergetic neutrons at a specific energy Erefenergy,
Eref, required to produce the same displacement damage in a specified irradiated material, mat, as Φ(E).
Available from International Commission on Radiation Units and Measurements, 7910 Woodmont Avenue Suite 400 Bethesda, MD 20841-3095, http://www.icru.org/
E722 − 19
3.1.4.1 Discussion—
Note that Φ is equivalent to Φ(E) if, and only if, the specific device effect (for example, current gain degradation in silicon)
eq,Eref,mat
being correlated is described by the displacement damage function used in the calculation.
3.1.5 fluence andfluence spectrum—see neutron fluence and neutron fluence spectrum.
3.1.6 kerma factor—(K (E)) the kerma per unit fluence of particles of energy E present in a specified material, mat. See
mat
Terminology E170 for the definition of kerma, and a formula for calculating the kerma factor.
3.1.6.1 Discussion—
When a material is irradiated by a neutron field, the energy imparted to charged particles in the material may be described by the
kerma. The kerma may be divided into two parts, ionization kerma and displacement kerma. See 3.1.2.1 for the distinction between
kerma factor and microscopic kerma factor. Calculations of ionization and microscopic displacement kerma in silicon and gallium
arsenide as a result of irradiation by neutrons with energies up to 20 MeV are described in Refs 5-8 and in the annexes.
3.1.7 neutron fluence and neutron fluence spectrum are used in this standard, and are special cases of fluence and fluence
spectrum as defined in E170.
3.1.7.1 Discussion—
In cases where the context makes clear that neutrons are referred to, the terms fluence and fluence spectrum are sometimes used.
4. Summary of Practice
4.1 The equivalent monoenergetic neutron fluence,
Φ , is given as follows:
eq,Eref,mat
`
* Φ~E!F ~E!dE
D,mat
Φ 5 (1)
eq,Eref,mat
F
D,Eref,mat
where:
Φ(E) = incident neutron fluence spectrum,
F (E) = neutron displacement damage function for the irradiated material (displacement damage per unit fluence) as a
D,mat
function of energy, and
F = displacement damage reference value designated for the irradiated material and for the specified equivalent energy,
D,Eref,mat
Eref, as given in the annexes.
The energy limits on the integral are determined in practice by the incident neutron fluence spectrum and by the material being
irradiated.
4.2 The neutron spectrum hardness parameter, H , is given as follows:
Eref,mat
`
Φ~E!F ~E!dE
*
D,mat
H 5 (2)
Eref,mat `
F Φ E dE
* ~ !
D,Eref,mat
4.3 Once the neutron fluence spectrum has been determined (for example, in accordance with Test Method E721) and the
equivalent monoenergetic fluence calculated, then a monitor (such as an activation foil) can be used in subsequent irradiations at
the same location to determine the fluence; that is, the neutron fluence is then described in terms of the equivalent monoenergetic
neutron fluence per unit monitor response, Φ /M . Use of a monitor foil to predict Φ is valid only if the neutron
eq,Eref,mat r eq,Eref,mat
spectrum remains constant.
5. Significance and Use
5.1 This practice is important in characterizing the radiation hardness of electronic devices irradiated by neutrons. This
characterization makes it feasible to predict some changes in operational properties of irradiated semiconductor devices or
electronic systems. To facilitate uniformity of the interpretation and evaluation of results of irradiations by sources of different
fluence spectra, it is convenient to reduce the incident neutron fluence from a source to a single parameter—an equivalent
monoenergetic neutron fluence—applicable to a particular semiconductor material.
5.2 In order to determine an equivalent monoenergetic neutron fluence, it is necessary to evaluate the displacement damage of
the particular semiconductor material. Ideally, this quantity is correlated to the degradation of a specific functional performance
parameter (such as current gain) of the semiconductor device or system being tested. However, this correlation has not been
established unequivocally for all device types and performance parameters since, in many instances, other effects also can be
E722 − 19
important. Ionization effects produced by the incident neutron fluence or by gamma rays in a mixed neutron fluence, short-term
and long-term annealing, and other factors can contribute to observed performance degradation (damage). Thus, caution should
be exercised in making a correlation between calculated displacement damage and performance degradation of a given electronic
device. The types of devices for which this correlation is applicable, and numerical evaluation of displacement damage are
discussed in the annexes.
5.3 The concept of 1-MeV equivalent fluence is widely used in the radiation-hardness testing community. It has merits and
disadvantages that have been debated widely (9-12). For these reasons, specifics of a standard application of the 1-MeV equivalent
fluence are presented in the annexes.
6. Procedure for Calculating Φ
eq,Eref,mat
6.1 To evaluate Eq 1 and 2, determine the energy limits E and E to be used in place of zero and infinity in the integrals
min max
of (Eq 1) and (Eq 2) and the values of the displacement damage function F (E) for the irradiated material and perform the
D,mat
indicated integrations.
6.1.1 Choose the upper limit E to be at an energy above which the integral damage falls to an insignificant level. For Godiva-
max
or TRIGA-type spectra, this limit is about 12 MeV.
6.1.2 Choose the lower-energy limit E to be at an energy below which the integral damage falls to an insignificant level. For
min
silicon irradiated by Godiva-type spectra, this energy has been historically chosen to be about 0.01 MeV. More highly moderated
spectra may require lower thresholds or specialized filtering requirements such as a boron shield, or both.
6.1.3 The values of the neutron displacement damage function used in Eq 1 and 2 obviously depend on the material and the
equivalent energy chosen. For silicon, resonance effects cause large variations (by a factor of 20 or more) in the displacement
damage function as a function of energy over the range from about 0.1 to 8 MeV (4, 5). Therefore, monoenergetic neutron sources
with these energies may not be useful for effects testing. Also, for a selected equivalent energy, the value of F at that
D,Eref,mat
specific energy may not be representative of the displacement damage function at nearby energies. In such cases, a method of
averaging the damage function over a range of energies around the chosen equivalent energy can be used. Such averaging is
discussed in the annexes. Because the F (E) term is normalized by dividing by F in Eq 1 and 2, only the shape of the
D,mat D,Eref,mat
F (E) function versus energy is of primary importance. In such a case, precise knowledge of the absolute values of F (E)
D,mat D,mat
is not required in evaluating Φ and H .
eq,Eref,mat Eref,mat
7. Determining Φ with a Monitor Foil
eq,Eref,mat
7.1 At the same time that the fluence spectrum, Φ(E), of the source is determined (for example, with an activation foil set in
accordance with Guides E720 or E844, or both, and Test Method E721 or Practice E944, or both) place a fast-neutron monitor foil
in the neutron field at an appropriate location. After Φ is determined and the monitor foil counted, calculate the ratio of
eq,Eref,mat
the equivalent monoenergetic fluence to the unit monitor response, Φ /M .
eq,Eref,mat r
7.2 Use the response of the fast-neutron monitor foil, M , to predict Φ in subsequent routine device test irradiations.
r eq,Eref,mat
For this method to be valid, it is important to keep the source-foil geometry essentially identical to that used for calibrating the
monitor foil. Moderate changes in source-to-foil distance are allowable. In addition, make sure the source location (of a
Godiva-type reactor) with respect to scattering materials (walls, floor, etc.) is the same. Do not change or move nearby scattering
materials or moderators.
7.3 Precautions in maintaining original calibration conditions are necessary to avoid altering the neutron fluence spectrum
significantly in subsequent irradiations. An appreciable change in the spectrum will invalidate the calibration of the monitor foil
and, therefore, would necessitate a new measurement of Φ(E) and recalibration of the monitor foil. Whenever the neutron source
configuration is changed, as for example, if the core fuel elements are replaced or rearranged in a nuclear reactor, the activation
foil spectrum measurements and all quantities derived from them may need to be remeasured.
7.4 The choice of a monitor foil material depends on several factors:
7.4.1 The activation threshold should be high enough so as to make it insensitive to neutrons below the E value used in Eq
min
1 and 2. However, the threshold energy should be low enough to sample a significant fraction of the total fluence.
7.4.2 The monitor foil should have a high neutron sensitivity and a convenient half-life.
7.4.3 The detector system available for counting the monitor foil may dictate the choice of foil material. A germanium
54 58
gamma-ray detector system can be used, and Fe or Ni foils utilized as monitors. However, if a beta particle detector system
is available, then S foils are suitable. Details of the use of sulfur foils are given in Test Method E265.
8. Report
8.1 In the report of the results of radiation-hardness tests in which an equivalent monoenergetic neutron fluence is calculated,
the report should include at least the following information:
8.1.1 Semiconductor material and device performance parameter (for example, current gain in silicon bipolar transistors)
degradation being correlated to displacement damage should be specified.
8.1.2 Neutron source as to type and mode of operation during tests (fast-pulse or steady state).
E722 − 19
8.1.3 Neutron fluence spectrum and how it was determined.
8.1.4 Monitor foil employed and the detector system used for counting the foil. If an effective fission cross section for the
monitor foil is used, its value should be stated.
8.1.5 The neutron displacement damage function should be given, or referenced. The specific material (for example, silicon)
whose applicable damage function was used must be specified. The values cited in Annex A1 and Annex A2 shall be used for
silicon and GaAs, respectively.
8.1.6 Methods used for determining the average value of F and the value of Eref selected. The values cited in Annex
D,Eref,mat
A1 and Annex A2 shall be used for silicon and GaAs, respectively.
8.1.7 Method used for evaluating the integrals of Eq 1 and 2 (for example, the energy bin width and number of bins in a
numerical integration, and the limits of integration).
8.1.8 Values of Φ , H , and Φ /M .
eq,Eref,mat Eref,mat eq,Eref,mat r
9. Precision and Bias
9.1 The precision in calculating Φ and H will depend on the method of evaluation of the integrals in Eq 1 and
eq,Eref,mat Eref,mat
2 (for example, the width of the energy bins used in a numerical integration).
9.2 The uncertainty of the calculated results depends on (1) knowledge of the neutron fluence spectrum, (2) knowledge of the
displacement damage functions over that energy spectrum, and (3) knowledge of the value of the average displacement damage
function at the specified equivalent energy.
9.3 A specific example of the uncertainty associated with the calculation of a 1-MeV equivalent fluence for silicon is given in
Annex A1.
10. Keywords
10.1 displacement damage; electronic hardness; gallium arsenide; hardness parameter; silicon; silicon damage; silicon
equivalent damage (SED); 1–MeV equivalent fluence
ANNEXES
(Mandatory Information)
A1. CALCULATION OF 1-MeV EQUIVALENT NEUTRON FLUENCE FOR SILICON
A1.1 Background
A1.1.1 The observable damage metric of interest in this annex is the change in gain of a silicon bipolar junction transistor (BJT)
due to bulk displacement damage effects. The damage mechanism is the change in minority-carrier recombination lifetime in the
bulk semiconductor material. While a BJT gain may also be degraded by oxide traps and interface states introduced by the ionizing
dose to the oxide, this is a surface effect and is not within the scope of this standard. In interpreting measurements of this
1-MeV(Si) damage, efforts must be made to eliminate any interference from ionization-related surface effects.
A1.1.2 The choice of the specific energy for determining an equivalent fluence has been the subject of some controversy within
the electronics hardness-testing community (9). Some workers (10) have proposed that 1 MeV be used while others (11, 12) have
suggested 14 MeV to be more appropriate. The concept of 1-MeV equivalent fluence has gained broad acceptance in practice, and
procedures for applying it to silicon are described in this annex in some detail.
A1.1.3 An important basis of the practice is the correlation of radiation damage effects in a semiconductor device with the
displacement kerma produced in bulk silicon by neutron irradiation. This correlation assumes that volume (versus surface) effects
are the dominant radiation damage mechanism. Experimental evidence indicates that displacement kerma is a valid measure of
device performance degradation (for example, reduction in current gain) in bipolar transistors whose operation basically depends
on volume mechanisms (13, 14). However, for device types governed by surface phenomena (such as MOSFET devices), it is clear
that this correlation is not valid. Surface-effect devices are more sensitive than are volume-effect devices to ionization radiation
effects produced either by a neutron field or a mixed neutron-gamma field. Therefore, the basic mechanism associated with device
performance and the effect being correlated (for example, gain degradation) should be kept in mind before applying this practice
at any equivalent energy.
E722 − 19
A1.2 Calculation of Φ
eq,1MeV,Si
A1.2.1 The displacement damage function, F (E), defined for silicon in this annex is the silicon microscopic displacement
D,mat
kerma factor, as tabulated in Table A1.1.
A1.2.2 A 1-MeV equivalent fluence in silicon is defined for an irradiation by neutrons of any neutron spectrum for which the
predominant source of displacement damage is from neutrons of energy between 10 keV and 20 MeV. The neutron fluence
spectrum, Φ(E), may be that determined from a neutron transport calculation, that determined from measurements, or that given
in an environment specification document.
A1.2.3 The neutron fluence spectrum, Φ(E), may be determined experimentally by measuring a set of activation foils and then by
application of a spectral adjustment computer code (see Guide E720 and Test Method E721 for details).
A1.2.4 Results of calculations of silicon microscopic displacement kerma factors (displacement kerma per target atom per unit
−10
neutron fluence), κ (E), are given in Table A1.1 as a function of neutron energy over the range from 10 to 20 MeV ((15).).
D,Si
The unit of the microscopic kerma factor is megaelectron volt times millibarns (MeV·mbarn). Each factor can be multiplied by
−13 2 −19 2 2
3.435 × 10 to convert to rad(Si)·cm , or by 3.435 × 10 to convert to J·m /kg or Gy(Si)·m . The silicon microscopic
displacement kerma factor as given in Table A1.1 is the accepted silicon damage function to be used in the application of this
standard: F ~E!5κ ~E!. This microscopic displacement kerma was computed by using the ENDF/B-VIIENDF/B-VIII.0 cross
D,Si D,Si
28 29 30
sections ((16)) for Si, Si and Si in their natural abundance composition, a displacementcomposition shown in Table
A1.2threshold energy of 20.5 eV, , the Robinson fit to the Lindhard energy partition function ((17),), and the NJOY-2012
processing code ((18).). The elemental silicon atomic weight of 28.085 amu is used for the elemental silicon lattice atom atomic
weight (19) and it is converted from amu into neutron mass units before it is used in the Robinson formalism of the partition
function. Fig. A1.1 shows the energy dependence of the silicon 1-MeV damage function.
A1.2.5 An average value of neutron microscopic displacement kerma factor near 1 MeV is difficult to determine because of sharp
neutron cross-section resonances in that energy region. To avoid these difficulties, Namenson, Wolicki, and Messenger (13) fitted
the function AEA·E(1 − exp(− B/E)) to various tabulations of κ (E) versus energy. The values of A and B obtained by a least
D
squares fit yielded an average value at 1 MeV of 95 6 4 MeV·mbarn. A similar procedure applied to the data given in Table A1.1
also gives a value close to 95 MeV·mbarn.MeV·mbarn (22). Accordingly, the designated value of F to be used in Eq 1
D,1MeV,Si
and 2 to calculate a 1-MeV equivalent fluence is 95 MeV·mbarn.
A1.2.6 For purposes of intercomparison of hardness testing results from various laboratories, the value of F used in
D,1MeV,Si
obtaining such results is very important; therefore, reporting of results should include confirmation that the value of F
D,1MeV,Si
designated in A1.2.5 was used in any calculation.
A1.2.7 Once the neutron fluence spectrum Φ(E) has been determined for the energy range of interest, then use numerical
integration to evaluate Eq 1 and 2, using values for F (E) from Table A1.1 and F = 95 MeV·mbarn.
D D,1MeV,Si
A1.3 Precision and Bias
A1.3.1 The values for κ (E) given in Table A1.1 are determined by calculating the total kerma displacement kerma using the
D,Si
methodology implemented in the NJOY-2012 code (18), and then partitioning it into ionization and displacement fractions.
fractions using the Robinson partition function (17). Because of the lack of adequate theory to perform the partition of the kerma
and due to the uncertainties in cross sections, the estimated uncertainty in the microscopic displacement kerma factor is about 10 %
up to 3 MeV.MeV (22, 23). Correlation of the microscopic displacement kerma with measured damage in many neutron fields has
been confirmed with uncertainties no larger than 10 % (14).
A1.3.2 Uncertainties in the neutron fluence spectrum, Φ(E), will vary based on the method used to obtain it. If neutron sensors
such as activation foils were used, see Standard Guide E721.
A1.3.3 Since this mandatory annex requires the use of Table A1.1 and F = 95 MeV·mbarn, no uncertainty in the
D,1MeV,Si
calculation of 1-MeV equivalent fluence is attributable to the consistent use of these data. Therefore only the uncertainty in the
determination of Φ(E) need be considered in assigning an uncertainty to the 1-MeV equivalent fluence. An uncertainty in the
E722 − 19
nat
TABLE A1.1 Silicon Damage Function
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
1 2.000000E+01 1.995000E+01 1.974223E+02
1 2.000000E+01 1.995000E+01 1.973868E+02
2 1.990000E+01 1.985000E+01 1.967937E+02
2 1.990000E+01 1.985000E+01 1.967664E+02
3 1.980000E+01 1.975000E+01 1.961647E+02
3 1.980000E+01 1.975000E+01 1.961368E+02
4 1.970000E+01 1.965000E+01 1.955857E+02
4 1.970000E+01 1.965000E+01 1.955665E+02
5 1.960000E+01 1.955000E+01 1.952768E+02
5 1.960000E+01 1.955000E+01 1.952573E+02
6 1.950000E+01 1.945000E+01 1.950267E+02
6 1.950000E+01 1.945000E+01 1.950075E+02
7 1.940000E+01 1.935000E+01 1.949968E+02
7 1.940000E+01 1.935000E+01 1.949787E+02
8 1.930000E+01 1.925000E+01 1.951260E+02
8 1.930000E+01 1.925000E+01 1.951091E+02
9 1.920000E+01 1.915000E+01 1.955842E+02
9 1.920000E+01 1.915000E+01 1.955607E+02
10 1.910000E+01 1.905000E+01 1.969098E+02
10 1.910000E+01 1.905000E+01 1.968811E+02
11 1.900000E+01 1.895000E+01 1.982156E+02
11 1.900000E+01 1.895000E+01 1.981732E+02
12 1.890000E+01 1.885000E+01 1.991628E+02
12 1.890000E+01 1.885000E+01 1.991148E+02
13 1.880000E+01 1.875000E+01 1.999799E+02
13 1.880000E+01 1.875000E+01 1.999262E+02
14 1.870000E+01 1.865000E+01 1.978047E+02
14 1.870000E+01 1.865000E+01 1.977638E+02
15 1.860000E+01 1.855000E+01 1.938940E+02
15 1.860000E+01 1.855000E+01 1.938703E+02
16 1.850000E+01 1.845000E+01 1.920378E+02
16 1.850000E+01 1.845000E+01 1.920284E+02
17 1.840000E+01 1.835000E+01 1.930547E+02
17 1.840000E+01 1.835000E+01 1.930398E+02
18 1.830000E+01 1.825000E+01 1.941904E+02
18 1.830000E+01 1.825000E+01 1.941703E+02
19 1.820000E+01 1.815000E+01 1.956167E+02
19 1.820000E+01 1.815000E+01 1.955830E+02
20 1.810000E+01 1.805000E+01 1.964416E+02
20 1.810000E+01 1.805000E+01 1.963928E+02
21 1.800000E+01 1.795000E+01 1.941766E+02
21 1.800000E+01 1.795000E+01 1.941498E+02
22 1.790000E+01 1.785000E+01 1.917115E+02
22 1.790000E+01 1.785000E+01 1.916968E+02
23 1.780000E+01 1.775000E+01 1.905113E+02
23 1.780000E+01 1.775000E+01 1.904943E+02
24 1.770000E+01 1.765000E+01 1.897319E+02
24 1.770000E+01 1.765000E+01 1.897224E+02
25 1.760000E+01 1.755000E+01 1.907675E+02
25 1.760000E+01 1.755000E+01 1.907523E+02
26 1.750000E+01 1.745000E+01 1.921653E+02
26 1.750000E+01 1.745000E+01 1.921376E+02
27 1.740000E+01 1.735000E+01 1.923810E+02
27 1.740000E+01 1.735000E+01 1.923461E+02
28 1.730000E+01 1.725000E+01 1.922374E+02
28 1.730000E+01 1.725000E+01 1.922046E+02
29 1.720000E+01 1.715000E+01 1.924440E+02
29 1.720000E+01 1.715000E+01 1.924038E+02
30 1.710000E+01 1.705000E+01 1.926999E+02
30 1.710000E+01 1.705000E+01 1.926536E+02
31 1.700000E+01 1.695000E+01 1.921279E+02
31 1.700000E+01 1.695000E+01 1.920722E+02
32 1.690000E+01 1.685000E+01 1.915772E+02
32 1.690000E+01 1.685000E+01 1.915217E+02
33 1.680000E+01 1.675000E+01 1.937092E+02
33 1.680000E+01 1.675000E+01 1.936340E+02
34 1.670000E+01 1.665000E+01 1.953922E+02
34 1.670000E+01 1.665000E+01 1.952966E+02
35 1.660000E+01 1.655000E+01 1.903341E+02
35 1.660000E+01 1.655000E+01 1.902622E+02
36 1.650000E+01 1.645000E+01 1.856649E+02
36 1.650000E+01 1.645000E+01 1.856090E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
37 1.640000E+01 1.635000E+01 1.865918E+02
37 1.640000E+01 1.635000E+01 1.865312E+02
38 1.630000E+01 1.625000E+01 1.877974E+02
38 1.630000E+01 1.625000E+01 1.877142E+02
39 1.620000E+01 1.615000E+01 1.883864E+02
39 1.620000E+01 1.615000E+01 1.882977E+02
40 1.610000E+01 1.605000E+01 1.883452E+02
40 1.610000E+01 1.605000E+01 1.882490E+02
41 1.600000E+01 1.595000E+01 1.875458E+02
41 1.600000E+01 1.595000E+01 1.874403E+02
42 1.590000E+01 1.585000E+01 1.843038E+02
42 1.590000E+01 1.585000E+01 1.842194E+02
43 1.580000E+01 1.575000E+01 1.803025E+02
43 1.580000E+01 1.575000E+01 1.802182E+02
44 1.570000E+01 1.565000E+01 1.792159E+02
44 1.570000E+01 1.565000E+01 1.791307E+02
45 1.560000E+01 1.555000E+01 1.793850E+02
45 1.560000E+01 1.555000E+01 1.792942E+02
46 1.550000E+01 1.545000E+01 1.812501E+02
46 1.550000E+01 1.545000E+01 1.811301E+02
47 1.540000E+01 1.535000E+01 1.824167E+02
47 1.540000E+01 1.535000E+01 1.822846E+02
48 1.530000E+01 1.525000E+01 1.825359E+02
48 1.530000E+01 1.525000E+01 1.823885E+02
49 1.520000E+01 1.515000E+01 1.785266E+02
49 1.520000E+01 1.515000E+01 1.783886E+02
50 1.510000E+01 1.505000E+01 1.758240E+02
50 1.510000E+01 1.505000E+01 1.756900E+02
51 1.500000E+01 1.495000E+01 1.795943E+02
51 1.500000E+01 1.495000E+01 1.794274E+02
52 1.490000E+01 1.485000E+01 1.789953E+02
52 1.490000E+01 1.485000E+01 1.788293E+02
53 1.480000E+01 1.475000E+01 1.757235E+02
53 1.480000E+01 1.475000E+01 1.755598E+02
54 1.470000E+01 1.465000E+01 1.748468E+02
54 1.470000E+01 1.465000E+01 1.746830E+02
55 1.460000E+01 1.455000E+01 1.772119E+02
55 1.460000E+01 1.455000E+01 1.770211E+02
56 1.450000E+01 1.445000E+01 1.823635E+02
56 1.450000E+01 1.445000E+01 1.821349E+02
57 1.440000E+01 1.435000E+01 1.822088E+02
57 1.440000E+01 1.435000E+01 1.819542E+02
58 1.430000E+01 1.425000E+01 1.809770E+02
58 1.430000E+01 1.425000E+01 1.807217E+02
59 1.420000E+01 1.415000E+01 1.797454E+02
59 1.420000E+01 1.415000E+01 1.794793E+02
60 1.410000E+01 1.405000E+01 1.768178E+02
60 1.410000E+01 1.405000E+01 1.765542E+02
61 1.400000E+01 1.395000E+01 1.788456E+02
61 1.400000E+01 1.395000E+01 1.785629E+02
62 1.390000E+01 1.385000E+01 1.847664E+02
62 1.390000E+01 1.385000E+01 1.844297E+02
63 1.380000E+01 1.375000E+01 1.784289E+02
63 1.380000E+01 1.375000E+01 1.781225E+02
64 1.370000E+01 1.365000E+01 1.760411E+02
64 1.370000E+01 1.365000E+01 1.757290E+02
65 1.360000E+01 1.355000E+01 1.782104E+02
65 1.360000E+01 1.355000E+01 1.778709E+02
66 1.350000E+01 1.345000E+01 1.816978E+02
66 1.350000E+01 1.345000E+01 1.813241E+02
67 1.340000E+01 1.335000E+01 1.785120E+02
67 1.340000E+01 1.335000E+01 1.781406E+02
68 1.330000E+01 1.325000E+01 1.772619E+02
68 1.330000E+01 1.325000E+01 1.768893E+02
69 1.320000E+01 1.315000E+01 1.805299E+02
69 1.320000E+01 1.315000E+01 1.801226E+02
70 1.310000E+01 1.305000E+01 1.837276E+02
70 1.310000E+01 1.305000E+01 1.832955E+02
71 1.300000E+01 1.295000E+01 1.828576E+02
71 1.300000E+01 1.295000E+01 1.824153E+02
72 1.290000E+01 1.285000E+01 1.825162E+02
72 1.290000E+01 1.285000E+01 1.820566E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
73 1.280000E+01 1.275000E+01 1.831141E+02
73 1.280000E+01 1.275000E+01 1.826390E+02
74 1.270000E+01 1.265000E+01 1.812270E+02
74 1.270000E+01 1.265000E+01 1.807486E+02
75 1.260000E+01 1.255000E+01 1.735857E+02
75 1.260000E+01 1.255000E+01 1.731323E+02
76 1.250000E+01 1.245000E+01 1.767395E+02
76 1.250000E+01 1.245000E+01 1.762513E+02
77 1.240000E+01 1.235000E+01 1.797322E+02
77 1.240000E+01 1.235000E+01 1.792074E+02
78 1.230000E+01 1.225000E+01 1.790482E+02
78 1.230000E+01 1.225000E+01 1.785140E+02
79 1.220000E+01 1.215000E+01 1.787140E+02
79 1.220000E+01 1.215000E+01 1.781711E+02
80 1.210000E+01 1.205000E+01 1.759861E+02
80 1.210000E+01 1.205000E+01 1.754457E+02
81 1.200000E+01 1.195000E+01 1.743238E+02
81 1.200000E+01 1.195000E+01 1.737800E+02
82 1.190000E+01 1.185000E+01 1.730297E+02
82 1.190000E+01 1.185000E+01 1.724747E+02
83 1.180000E+01 1.175000E+01 1.727131E+02
83 1.180000E+01 1.175000E+01 1.721396E+02
84 1.170000E+01 1.165000E+01 1.742102E+02
84 1.170000E+01 1.165000E+01 1.736148E+02
85 1.160000E+01 1.155000E+01 1.752101E+02
85 1.160000E+01 1.155000E+01 1.746005E+02
86 1.150000E+01 1.145000E+01 1.739761E+02
86 1.150000E+01 1.145000E+01 1.733552E+02
87 1.140000E+01 1.135000E+01 1.710272E+02
87 1.140000E+01 1.135000E+01 1.703988E+02
88 1.130000E+01 1.125000E+01 1.668493E+02
88 1.130000E+01 1.125000E+01 1.662376E+02
89 1.120000E+01 1.115000E+01 1.656722E+02
89 1.120000E+01 1.115000E+01 1.650580E+02
90 1.110000E+01 1.105000E+01 1.709562E+02
90 1.110000E+01 1.105000E+01 1.702935E+02
91 1.100000E+01 1.095000E+01 1.736557E+02
91 1.100000E+01 1.095000E+01 1.729656E+02
92 1.090000E+01 1.085000E+01 1.737472E+02
92 1.090000E+01 1.085000E+01 1.730395E+02
93 1.080000E+01 1.075000E+01 1.699377E+02
93 1.080000E+01 1.075000E+01 1.692476E+02
94 1.070000E+01 1.065000E+01 1.650493E+02
94 1.070000E+01 1.065000E+01 1.643638E+02
95 1.060000E+01 1.055000E+01 1.671501E+02
95 1.060000E+01 1.055000E+01 1.664527E+02
96 1.050000E+01 1.045000E+01 1.683353E+02
96 1.050000E+01 1.045000E+01 1.676141E+02
97 1.040000E+01 1.035000E+01 1.743913E+02
97 1.040000E+01 1.035000E+01 1.736229E+02
98 1.030000E+01 1.025000E+01 1.736199E+02
98 1.030000E+01 1.025000E+01 1.728499E+02
99 1.020000E+01 1.015000E+01 1.752688E+02
99 1.020000E+01 1.015000E+01 1.744761E+02
100 1.010000E+01 1.005000E+01 1.731668E+02
100 1.010000E+01 1.005000E+01 1.723774E+02
101 1.000000E+01 9.950000E+00 1.749790E+02
101 1.000000E+01 9.950000E+00 1.741678E+02
102 9.900000E+00 9.850000E+00 1.725378E+02
102 9.900000E+00 9.850000E+00 1.717298E+02
103 9.800000E+00 9.750000E+00 1.680329E+02
103 9.800000E+00 9.750000E+00 1.672486E+02
104 9.700000E+00 9.650000E+00 1.643838E+02
104 9.700000E+00 9.650000E+00 1.636157E+02
105 9.600000E+00 9.550000E+00 1.737880E+02
105 9.600000E+00 9.550000E+00 1.729551E+02
106 9.500000E+00 9.450000E+00 1.790983E+02
106 9.500000E+00 9.450000E+00 1.782361E+02
107 9.400000E+00 9.350000E+00 1.719788E+02
107 9.400000E+00 9.350000E+00 1.711540E+02
108 9.300000E+00 9.250000E+00 1.585817E+02
108 9.300000E+00 9.250000E+00 1.578282E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
109 9.200000E+00 9.150000E+00 1.642940E+02
109 9.200000E+00 9.150000E+00 1.635106E+02
110 9.100000E+00 9.050000E+00 1.840511E+02
110 9.100000E+00 9.050000E+00 1.831674E+02
111 9.000000E+00 8.950000E+00 1.844116E+02
111 9.000000E+00 8.950000E+00 1.835292E+02
112 8.900000E+00 8.850000E+00 1.649178E+02
112 8.900000E+00 8.850000E+00 1.641407E+02
113 8.800000E+00 8.750000E+00 1.543472E+02
113 8.800000E+00 8.750000E+00 1.536291E+02
114 8.700000E+00 8.650000E+00 1.719501E+02
114 8.700000E+00 8.650000E+00 1.711415E+02
115 8.600000E+00 8.550000E+00 1.726602E+02
115 8.600000E+00 8.550000E+00 1.718448E+02
116 8.500000E+00 8.450000E+00 1.737737E+02
116 8.500000E+00 8.450000E+00 1.729498E+02
117 8.400000E+00 8.350000E+00 1.725798E+02
117 8.400000E+00 8.350000E+00 1.717610E+02
118 8.300000E+00 8.250000E+00 1.702067E+02
118 8.300000E+00 8.250000E+00 1.693958E+02
119 8.200000E+00 8.150000E+00 1.629746E+02
119 8.200000E+00 8.150000E+00 1.622010E+02
120 8.100000E+00 8.050000E+00 1.776760E+02
120 8.100000E+00 8.050000E+00 1.768217E+02
121 8.000000E+00 7.950000E+00 1.951620E+02
121 8.000000E+00 7.950000E+00 1.942243E+02
122 7.900000E+00 7.850000E+00 1.818550E+02
122 7.900000E+00 7.850000E+00 1.809926E+02
123 7.800000E+00 7.750000E+00 1.819305E+02
123 7.800000E+00 7.750000E+00 1.810599E+02
124 7.700000E+00 7.650000E+00 1.750185E+02
124 7.700000E+00 7.650000E+00 1.741924E+02
125 7.600000E+00 7.550000E+00 1.721660E+02
125 7.600000E+00 7.550000E+00 1.713542E+02
126 7.500000E+00 7.450000E+00 1.750415E+02
126 7.500000E+00 7.450000E+00 1.742301E+02
127 7.400000E+00 7.350000E+00 1.771959E+02
127 7.400000E+00 7.350000E+00 1.763690E+02
128 7.300000E+00 7.250000E+00 1.762695E+02
128 7.300000E+00 7.250000E+00 1.754672E+02
129 7.200000E+00 7.150000E+00 1.436002E+02
129 7.200000E+00 7.150000E+00 1.429532E+02
130 7.100000E+00 7.050000E+00 1.734795E+02
130 7.100000E+00 7.050000E+00 1.727034E+02
131 7.000000E+00 6.950000E+00 1.482196E+02
131 7.000000E+00 6.950000E+00 1.475553E+02
132 6.900000E+00 6.850000E+00 1.534783E+02
132 6.900000E+00 6.850000E+00 1.528027E+02
133 6.800000E+00 6.750000E+00 1.735103E+02
133 6.800000E+00 6.750000E+00 1.727339E+02
134 6.700000E+00 6.650000E+00 1.573224E+02
134 6.700000E+00 6.650000E+00 1.566315E+02
135 6.600000E+00 6.550000E+00 1.287192E+02
135 6.600000E+00 6.550000E+00 1.281781E+02
136 6.500000E+00 6.450000E+00 1.476404E+02
136 6.500000E+00 6.450000E+00 1.469991E+02
137 6.400000E+00 6.350000E+00 1.597855E+02
137 6.400000E+00 6.350000E+00 1.590746E+02
138 6.300000E+00 6.250000E+00 1.843861E+02
138 6.300000E+00 6.250000E+00 1.835404E+02
139 6.200000E+00 6.150000E+00 1.327218E+02
139 6.200000E+00 6.150000E+00 1.321562E+02
140 6.100000E+00 6.050000E+00 1.618680E+02
140 6.100000E+00 6.050000E+00 1.611566E+02
141 6.000000E+00 5.950000E+00 1.427187E+02
141 6.000000E+00 5.950000E+00 1.421075E+02
142 5.900000E+00 5.850000E+00 1.741425E+02
142 5.900000E+00 5.850000E+00 1.733649E+02
143 5.800000E+00 5.750000E+00 1.877007E+02
143 5.800000E+00 5.750000E+00 1.868717E+02
144 5.700000E+00 5.650000E+00 1.566230E+02
144 5.700000E+00 5.650000E+00 1.559314E+02
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
145 5.600000E+00 5.550000E+00 1.521489E+02
145 5.600000E+00 5.550000E+00 1.514860E+02
146 5.500000E+00 5.450000E+00 1.239832E+02
146 5.500000E+00 5.450000E+00 1.234471E+02
147 5.400000E+00 5.350000E+00 1.296535E+02
147 5.400000E+00 5.350000E+00 1.290942E+02
148 5.300000E+00 5.250000E+00 1.558386E+02
148 5.300000E+00 5.250000E+00 1.551565E+02
149 5.200000E+00 5.150000E+00 1.773568E+02
149 5.200000E+00 5.150000E+00 1.765639E+02
150 5.100000E+00 5.050000E+00 1.558377E+02
150 5.100000E+00 5.050000E+00 1.551267E+02
151 5.000000E+00 4.950000E+00 1.523304E+02
151 5.000000E+00 4.950000E+00 1.516193E+02
152 4.900000E+00 4.850000E+00 1.659307E+02
152 4.900000E+00 4.850000E+00 1.651634E+02
153 4.800000E+00 4.750000E+00 1.936596E+02
153 4.800000E+00 4.750000E+00 1.927708E+02
154 4.700000E+00 4.650000E+00 1.615820E+02
154 4.700000E+00 4.650000E+00 1.608431E+02
155 4.600000E+00 4.550000E+00 1.446275E+02
155 4.600000E+00 4.550000E+00 1.439489E+02
156 4.500000E+00 4.450000E+00 1.454466E+02
156 4.500000E+00 4.450000E+00 1.447625E+02
157 4.400000E+00 4.350000E+00 1.391803E+02
157 4.400000E+00 4.350000E+00 1.385367E+02
158 4.300000E+00 4.250000E+00 1.718335E+02
158 4.300000E+00 4.250000E+00 1.710236E+02
159 4.200000E+00 4.150000E+00 1.106764E+02
159 4.200000E+00 4.150000E+00 1.101688E+02
160 4.100000E+00 4.050000E+00 1.377047E+02
160 4.100000E+00 4.050000E+00 1.370340E+02
161 4.000000E+00 3.950000E+00 1.398655E+02
161 4.000000E+00 3.950000E+00 1.392049E+02
162 3.900000E+00 3.850000E+00 1.143880E+02
162 3.900000E+00 3.850000E+00 1.138522E+02
163 3.800000E+00 3.750000E+00 1.189786E+02
163 3.800000E+00 3.750000E+00 1.184181E+02
164 3.700000E+00 3.650000E+00 7.205235E+01
164 3.700000E+00 3.650000E+00 7.169035E+01
165 3.600000E+00 3.550000E+00 1.166491E+02
165 3.600000E+00 3.550000E+00 1.160873E+02
166 3.500000E+00 3.450000E+00 1.209489E+02
166 3.500000E+00 3.450000E+00 1.203618E+02
167 3.400000E+00 3.350000E+00 1.171509E+02
167 3.400000E+00 3.350000E+00 1.166044E+02
168 3.300000E+00 3.250000E+00 1.233782E+02
168 3.300000E+00 3.250000E+00 1.228177E+02
169 3.200000E+00 3.150000E+00 1.371566E+02
169 3.200000E+00 3.150000E+00 1.364921E+02
170 3.100000E+00 3.050000E+00 1.225885E+02
170 3.100000E+00 3.050000E+00 1.219693E+02
171 3.000000E+00 2.950000E+00 1.017558E+02
171 3.000000E+00 2.950000E+00 1.012464E+02
172 2.900000E+00 2.850000E+00 1.380089E+02
172 2.900000E+00 2.850000E+00 1.373463E+02
173 2.800000E+00 2.750000E+00 1.104907E+02
173 2.800000E+00 2.750000E+00 1.099198E+02
174 2.700000E+00 2.650000E+00 1.185021E+02
174 2.700000E+00 2.650000E+00 1.178785E+02
175 2.600000E+00 2.550000E+00 1.324304E+02
175 2.600000E+00 2.550000E+00 1.317324E+02
176 2.500000E+00 2.450000E+00 1.213907E+02
176 2.500000E+00 2.450000E+00 1.207865E+02
177 2.400000E+00 2.350000E+00 1.059031E+02
177 2.400000E+00 2.350000E+00 1.053801E+02
178 2.300000E+00 2.250000E+00 1.077988E+02
178 2.300000E+00 2.250000E+00 1.072764E+02
179 2.200000E+00 2.150000E+00 1.108041E+02
179 2.200000E+00 2.150000E+00 1.102115E+02
180 2.100000E+00 2.050000E+00 9.770454E+01
180 2.100000E+00 2.050000E+00 9.719414E+01
E722 − 19
TABLE A1.1 Continued
Displacement
Upper Energy Energy
Bin Damage
Bound Mid-point
Number Function
(MeV) (MeV)
(MeV·mbarn)
181 2.000000E+00 1.950000E+00 1.330953E+02
181 2.000000E+00 1.950000E+00 1.323761E+02
182 1.900000E+00 1.850000E+00 1.348081E+02
182 1.900000E+00 1.850000E+00 1.340592E+02
...